I am still experimenting and it takes a long time to tell whether a particular strategy actually works until you get to 1945.
But here are my general observations.
UK Initially build lots of merchant ships, escorts, inf divisions, and landing crafts. With skills into escorts and detection.
You have to concentrate on anti-sub warfare until you are sure the Germans aren't mounting a major shipping attack. It may be a waste but if the Germans do push subs and you don't push anti-sub you may find your supply system destroyed in 40/41.
The infantry divisions are needed to cover ports until you are strong enough and the game has advance far enough you don't have to worry about invasion. Also, the divisions allow you use some of your bigger units to reinforce Africa.
Landing craft give you flexibility to strike at Germany, Italy or North Africa if the Axis player doesn't garrison.
The UK has lots of logistics so I try to make some Strategic bombers.
US I find the US ground forces very weak compared to German or even UK because they start a such low experience levels. I usually concentrate more on air power with enough armor/infantry to support the UK forces.
Russia I am still experimenting with building cavalry early. Lots fighters later to be ready in time for 41. Later I will break them up to build offensive units. But I don't have a lot of confidence in my ability to stop the Germans in 41/42.
Germany Early on I concentrate on air and subs (just to force the UK to expend their production countering). I aim for air superiority early with enough tactical air to support the breakthrough attacks in 41. I find air close support more flexible than armor for concentrating attacks. Oil is a problem though.
Italy Plan on Germany sending the oil to keep them active in Africa. There war ships are best used as a threat unless the UK is negligent in handling their fleets.
Allies in General
Strategic bombers targeting oil supplies seems to work well but it is difficult to judge the effectiveness of it since I haven't been on the receiving end of that tactic. If the Germans don't keep enough fighters in the west two UK, one US and one Russian long range bombers can knock out almost all oil production in Europe.
Lost of Landing Craft so you had the flexibility to strike anywhere anytime. US, UK and Canada.
Lots of air power if you want to invade Europe with certain success in mind.
Axis in General
Other than air power I haven't really come up with something I have confidence in.
I do build quite a bit of Landing Ship capacity for both Germany and Italy. It gives the Axis a way to create threats on multiple fronts. If the UK doesn't garrison enough of England you can punish them for that. As long as you don't do it to early and avoid taking London you can really mess them up. Also, it allows you to take out Greece and North Africa rather easily.
I support this with building Marine units for both Germany and Italy as well as more mountain corps for the fight in Greece and later in Russia.
General observation: I am finding Logistics the most limiting factor for all countries. By 44 almost all the countries surviving have built out their excess production and manpower but no Logistics to build anything other than structures like anti-air, coastal defenses, and trucks.