Those are common Axis practices that usually led the players I advised to success.

Axis have expensive units, which makes the economy the main early game concern. In this build order you prioritize economy early game. I recommend reading the forum guides or Wiki first if you're new.
Please don't start the game before reading the guide carefully.

Day 1
If food prices are under 6 per unit, buy 5+k food.
First, you check your country carefully and see how many non-city (rural) provinces produce each resource. You will boost oil and food with industry. If there is a resource that none of your rural provinces produces, boost that as the 3rd resource; boost metal as 3rd otherwise.
But first, you need to build production buildings. There are two resources you won't be boosting; in one of their cities, build Barracks (and upgrade to lv2 ASAP). If you managed to buy 5k food build a second barracks lv1 in the other. In the oil city, build Industry straight away (do it in the food city instead if no rural province produces food and two produce oil).
While two are busy with Barracks and one with Industry, you build aircraft factories in the two remainings. Once the lv1 air factories are complete, start building Industry.

Also, build Local Industry in all core rural (non-city) provinces that produce any resource.
At the start of the game, the only you research is infantry, motorized infantry, attack bomber and interceptor. Do not research anything else till day 3.
Produce infantry (4 max), but make sure the barracks are idle when mot infantry is researched, so you can produce as much mot infantry as possible (use queues if you can). One air factory will produce Interceptors, the other attack bombers.

Split the 2 armoured cars out and send them to merge with the mot infantry. There mustn’t be any other unit split out with the armoured cars, check the bar at the bottom to make sure.
Choose a player country (not an AI!) you’ll attack on day 2. Check the (i) button on players in Diplomacy to see their stats and try not to fight a high-level player (if you don’t understand this, just choose any opponent that has 5 cities).
Send all your troops to one province far from the border with the player. Don't move the troops already at the borders with your target, just not to look active or dangerous.

Day 2
By the end of day 2, you should have 5 mot infantry at least and 2 AC with them. Send all your Infantry to one border province with the target. If you’ve got more than 10 Infantry, the extra infantry should go to the border provinces with the enemy to defend against attacks. All Anti Air guns must be sent to protect the border provinces (AA guns are slow, so useless for attacks, but can add extra HP to the defending infantry).
Make sure you built an airstrip very close to the borders if there isn’t one already, and when you’re active, send the attack bombers there (to reveal enemy armies and destroy tanks as soon as you see them, don't direct attack the light tanks, patrol over them. It’ll work as long as you’re already at war. Make sure your attack bombers are all in a single army, also with interceptors if those have enough range.)
Make sure the 5+ mot infantry and 2 armoured cars are ONE army on the map, same about the 10 infantry.
The 10 infantry go forward and capture the nearest cities. Set waypoints so you don’t forget your infantry idle during the invasion.
The 5+ mot inf and 2 AC should go around and capture the furthest cities. Capture the capital as the last city.

If daychange is about to happen soon (within 5 hours) do not capture any of the cities, just leave the 10 infantry waiting very close to one city and the mot inf+AC waiting close to the far cities. Capture all of them through a single in-game day, the capital being the last one.
If you captured the capital first, the still enemy cities wouldn't get the bonus, if it wasn't through a single day, revolts would already happen at daychange. Following this advice, the morale bonus will remove the revolt chances. That’s useful as you’d need to leave units otherwise, and having a smaller army is an exponential disadvantage (X times smaller army=X*X times less instant strength).

Day 3
As soon as you defeat the player country, send some armies home. You should conquer two AI countries, to gain morale from capturing the capitals.
When fighting AI, have 1 Infantry in every border province with them except the one you’re attacking from. The main army should be at least 6 units. If their units are moving towards yours, stop your units in their way, let them ram into you and fight, and don't do anything. This way you’ll only be defending and gain a large advantage, assuming you’re using Infantry. Which is recommended, as you need mot infantry against difficult opponents.

You should have Industry lv2-3 in your oil, food and 3rd resource cities at this point. If not now, then once you do, start Industry in the two Barracks cities as well. Also, as soon as your manpower goes under 12k, start building recruiting stations in your core rural provinces that don’t produce a resource. The first wave should be 4-5 recruiting stations. You’ll have to cease food spending on mot inf, research medium tanks (MT) and produce them.
Also, build any new factories in non-core cities, not to slow down the economic buildup. Go all the way to industry lv5 in all core cities and local lv3 in all core rural provinces with resource production.

Later

If you have 10+ mot infantry, it’s worth researching lv3 and upgrading to there directly from lv1.
Produce units in such a balance to spend abundant resources; keep researching higher levels of the key units, and upgrading their factories. That way you can get a powerful army quickly. It’s recommended to add SP Artillery and Interceptors. If you want to add a new unit to the composition, consider building 3-4 lv1 factories for them and producing a lot of lv1’s quickly. Then, research higher levels and when your research is 6-10 days (of availability) ahead of lv1, upgrade all the lv1’s. For example, if lv1 is available from day 2 and your currently researched level is from day 10, you’re 8 days ahead.
To do this properly, choose the level X you want to direct-upgrade the lv1's to. Then, plan the research in such a way that, mainly, level X is complete as early as possible, but with lv2 being complete as late as possible (to give more space to the lv1 production).

Watch your terrain. If it’s very mountainous, it’s a good idea to focus on artillery and planes.
To protect yourself against airstrikes/artillery, add (SP)AA, and mainly, meatshield units. Those are lv1 militia for example. A large amount of them drastically reduces the damage other units receive, so the units will survive far longer and deal more damage. However, out of mountains, you don’t have so much time to fire with artillery and bombers before the enemy army can reach your stack, so slow large stacks get ineffective. Especially as Axis, which is pretty good at focusing on upgrading fewer units to max and getting a very effective army. Also, rocket fighters, however great the Axis buff is, aren’t very useful on large fronts or in offensives. They are a great defence against concentrated air push, though.

Axis has fairly fast units (esp. mot infantry and medium tanks). Consider adding high-level strat bombers, for long-range scouting and destroying the enemy factories quickly. When you attack the enemy, send all the land units (mot inf+MT) forward, and first, find the armies whose strength against attack bombers is the smallest compared to their strength against mot inf+MT. Attack those armies with attack bombers. If there are multiple, target the ones which are the closest to merging into a strong army first. If none of them are, target the smallest ones first. Again, planes to be stacked into groups of 10 planes per plane type (eg. 10 attack + 10 Ints, don't do with strats).
It's important to learn combat mechanics and check stats of the enemy units to determine which ones are the most dangerous. Target their factories with the strat bombers. Also, remember not to research too many units (submarines, naval bombers, attack bombers, interceptors, mot infantry, medium tanks is enough). For a non-coastal country, replace the naval bombers with SP Artillery which is great on land, many 10-stacks of them can create concentrated firepower to destroy large stacks. With strat bombers, Ints and activity, you'll be mostly able to destroy all enemy airforce. Be especially cautious with SP arty, which would get punished the hardest for no AA cover.

The followup, I feel, isn't considered early game anymore.

I don't focus on navy much as I tend to choose inland countries or ones with 2 core cities max on the coast. It's also quite possible to win without navy in any regular game, even the hardest ones have plenty of not very active players and transferring an army to another continent rarely fails. However, your point is definitely true, so here are some tips:

- If you aren't that dependent on water and want to save research time, research and produce cruisers only. They can be pretty strong if upgraded properly and stacked.

- Naval bombers are perfect for active players to defend large shorelines. They can all arrive to engage an enemy navy far quicker than any other naval unit, as long as you have proper air transfer. It's still good to have high-level subs too (especially with their Axis buff); while naval bombers deal with smaller attacks, concentrated subs can deal with cruiser or combined armies. Always remember that your damage is equally spread across the enemy army, so just 1 cruiser in a 10-sub army can cause more trouble to bombers than 5 cruisers alone.

- To save the research, you can replace naval bombers with attack bombers, which have roughly half the anti-navy value. They're well suited to be used as Axis, and most of the time you'll have them levelled up anyway. However, though all planes save any visible armies in range as intelligence reveals when patrolling, attack bombers can't reveal subs of the same or lower level, unlike naval bombers.

- If you leave a single naval bomber patrolling, it will save any army within view as an intelligence reveal. The patrol timer needn't run out (when the bomber would get killed by the defence of an enemy navy) for the reveal to be saved, so the first foreign army to enter your patrol's sight will always be saved, no matter what its damage against planes is. Notice that the reveals by spies or planes are cleared every daychange and that once the enemy army is out of view and starts displaying as a reveal, the reveal shows the whole path of the army, not just a fraction ending at a chokepoint (like when seeing it directly).

- Again, in combined armies, it's important to remember that the more units there are, the less of your damage each enemy unit receives. So, 10 submarines are harder to kill if you add 10 transport ships to them, as the transports (before they die) cause the subs to receive half the damage.
This you can make use of by making lv1 militia, researching lv4 transport ships and embarking the militia on them. You can add those to any navy, most helpful if added to ones fighting over chokepoints. You can also add militia to more valuable transports (like high-level units) to protect them. If you're planning a large landing, one way is to create a vast amount of lv1 militia and research lv4 transport ship, then merge the militia transports with the other transports and also all the navy you can afford to send away. This can be very hard to kill, really...

This is easy to say if you just play noob maps where no one knows the game, but this is an advanced guide, so it perhaps assumes you also have some good neighbours. As good players tend to have a superior strategy, they will usually wait to attack other skilled players on day 3 or later, when they can manage to completely adapt their army to the strategy. You aren't realizing how much impact it has to get +10% morale in all your provinces for the capital. You first attack a large country led by a weak player, then two AI, so the +20% morale even applies to the new cities you gained, and makes setting up production a lot easier. More production is helpful if you have to fight for survival, just stall your economy buildup and spam more units. If your enemy hasn't done the same thing the production for him will get a lot harder and he might get destroyed despite having comparable resource production.
The only weakness I see in this is the other countries sometimes take AI and there won't be two close ones. But, if you ready your units quick enough, you can attack just a while after you've captured all the cities of your main target, and scouting with the bombers helps to tell which AI you have to go for first, to prevent someone else from taking it.
Also, after the large attack, you'll be left with damaged infantry. Again, assuming you aren't playing an easy Clash map, you'll have good players close by. Infantry are better defending and aren't really fast, so they're easily outmanoeuvred. So, you use them to attack an AI (for profile stats nerds, you'll lose them to AI so it won't count to your player k/d ).

You think they will because you've never played a game where players really are active and skilled. Comintern are good in straight-up fights (those where both sides have roughly an equal army by resources spent and don't do any micromanagement). Of course it's easy for you, playing maps where no one knows how to play, to beat Comintern with Axis, as you can just avoid straight-up fights and engage where you have more power, which is supported by Lanchester's square law (a 2x stronger army is roughly 2x more effective in fights - in terms of how much damage it can deal while receiving a certain amount of damage back). Even though Comintern is usually considered a weaker doctrine, the difference is tiny, and a skilled player can manage to prevent Axis from picking a good fight, and force them into a straight-up one.
This, sorry, is quite the proof. Any good player knows that in competitive play, spreading out your power is foolish. If you want to succeed, rely on diplomacy and careful, detailed examination of the others' stats. This helps you tell which nation you could focus on, ideally make sure other nations aren't capable of quickly backstabbing you (which Sweden isn't as they're over water, a scout plane can tell you they're going for you 8 hours before they even disembark). A very good player has a solid army of fast-to-react units, which can help him in offensives, but can quickly be withdrawn and sent to deal with a sudden new danger. Mot infantry and especially planes are like that, you can focus on one enemy with them, but unlike slow units, you can also quickly send them anywhere else to defend against a new danger. Assuming you're active and scout with planes, you should see the new danger early enough to withdraw, but not early enough to also withdraw with infantry and such slower units.

This is just telling me that you're only playing against newbies, who can't make use of diplomacy and concentrate power to punish your focusing on 3 fronts at the same time. In a competitive game, you'd more often than not get destroyed when attacking France and Poland at the same time. Even if you win, a quick attack by another neighbour is very advantageous for him as he's taking a large chunk of land without having to fight many units, as you're almost powerless after the battle. Multiple neighbours may think this and you'll get divided between two or three countries.
But I admit that your strategy would sometimes work in World at War even, as there is also quite a few new players. But in a real battle of good players, it wouldn't.

As you mostly focus on subduing a weak neighbour and then two AI, it's good to have fast units to re-focus on different targets. Ordnance is good for defending chokepoints and advanced tactics, but it's slow, and wouldn't probably manage such quick changing of targets. Artillery also doesn't really benefit from Axis bonuses as it mostly bombards without taking damage, so the +15% health does not really help. Mot infantry is very good at taking care of enemy infantry, so I find it good despite its high food cost (you could sell the food). You, however, need to prevent larger armies of tanks, especially medium, as those are quite fast and strong against mot infantry. Though they could be outnumbered and destroyed early, if you let them merge, they're strong. In that situation, it's far better to have attack bombers, which can arrive quickly to destroy any tanks in range, than artillery, which are quite slow and can't keep up with the mot inf and catch the tanks, and are low hp on top of that (so not hard to destroy if you push forward). Attack bombers can destroy from an airport quite a distance behind, and you also have extra interceptors, which provide at least some protection against air counterattacks.

Agreed. I'm not expecting to encounter the best player in the world on day 1, and honestly, many will go inactive. So, if you really watch the profile stats carefully you can quite safely choose the weakest target. Then you ready your army and scout with planes, like 8 hours before the attack. If you see an exceptionally tough defence, you should retreat and pick the two AI instead, which boosts your economic and faster production potential. The objective of this guide is to lead you to an economically strong and fairly expanded nation by day 5, but it requires a lot of activity, which allows you to blitzkrieg effectively and even against quite good players. If active, you'll rarely have problems invading. It says "for active players" anyway. But most people aren't active enough for it, honestly. We all have our real lives.

It'd be tough, you have a point. But, if you're smart, you can manage to flank a mot infantry into their back quickly, so that they have 50% speed in their back instead of the same for you. Even if you can't do that, just wait for them to go forward to capture, and calculate it so your mot infantry get close to the enemy forward force (or arty if they have none) when you're about in the centre of a province. That way, they'll get 50% speed and even if they have something in front of them, they'll mostly get caught and destroyed. If on enemy territory you can't catch rocket arty with mot infantry, but once you reach the province centre you're suddenly 4x faster than them. Good luck hitting and running.
However, if they had a lot of infantry forward, it could be tough. What you can rely on is that there will never be rocket artillery before end of day 2 - even for Comintern, it takes 14 hours to research from D1 and reinforcements also take some time. So, before they manage a solid arty+rocket arty army you can have 10 mot infantry and 10 attack bombers. Attack bombers are an anti-tank unit, but if you spot their plans early enough, you can take advantage of numbers and snipe their artillery, too. But I admit, this is a tough situation to deal with. My build is a one focused on having good economy development, after all. The expansion is there just because it expects you to choose the weakest player according to stats. If you have a strong one nearby, perhaps they will ally, knowing you're Axis with a good buildup and large potential, or destroy you for the same reason.