Here is a list of best possible tactics for each of the five powers in the game. I came up with these tactics years ago (sometime around 1992) when I was still avidly playing the board game. You don't have to abide by the suggestions to the letter, but you can use these outlines as a guide for your play.
On the first turn, destroy what you can of the German navy.
This is to prevent the Germans from using naval power to destroy the British fleet and/or to use in the attack of Karelia.
Capture the Ukraine to increase pressure on the Germans and increase your own IPC income.
Fortify the eastern front to slow the Japanese advance.
Create and maintain a defensive posture (i.e. build infantry only) as it is much cheaper to produce and are much more useful to slow the German army.
On the first turn, destroy the British navy.
For any of the situations, if it is possible to supply extra firepower from any subs in the area, by all means use it to your advantage. This is to cripple the British fleet, delay D-day, and prevent a quick naval reply from the British to any German assaults on the Russians.
Attack and conquer Africa.
This is to cripple the British economy and cut off any relief forces going to and from the Suez Canal.
Assault the Russian front.
This is to destroy any Russian offensive capability and prevent a quick counterattack as well as preventing Russia from producing arms near the front by capturing Karelia. This blitz is needed as the Russians are the only ones who could tie down the German army.
Produce armor and infantry to support the eastern front and use the remaining naval and air forces to keep the British and American fleets in check. Try to defeat the Russians as fast as possible since the Germans will not be able to win a war of attrition at sea.
Destroy German navy if not done so already.
This is to remove the German fleet and prevent further German expansion out of Europe and/or prevents reinforcements for German troops already in Africa.
If possible, support Russian Attack/Defense.
This is to relieve the pressure on the Russians by supporting the Russian defense and/or gives the Germans more to think about by forming a second front or through diversionary attacks.
Maintain a defensive posture so as to lose as little territory as possible to the Axis. Produce air units and enough troops/transports so that the British will be able to capitalize on any defensive breaches in the Germans' "Fortress Europe". This is to attract the Germans attention and force them to divert precious troops and units from the eastern front.
Note: There is a maneuver called the Norman Naval Shield. It is used if the Germans have totally devastated the entire British navy. The UK stops building for one turn, while the Americans build transports. On the next turn, after clearing out the UK sea zone with allied fighters, the United Kingdom builds an aircraft carrier and a pair of fighters in the sea zone while the Americans move the transports from Eastern USA to Britain. This provides the necessary sea coverage required for the Allies to mount D-day.
Destroy all the naval powers in the immediate vicinity.
This is to maintain naval superiority and prevent the British or Americans from launching a deep strike into Japanese territory.
Attack the mainland. Either:
This is to slowly move inland and to force the Allies (Russians mostly) to worry about losing Asia, leaving the back door to Russia open.
Hold the Americans at bay with naval and air superiority where possible while focusing on the Asian mainland. This is to increase Japan's economic base and to weaken the Allies' economic power. Produce infantry to fight on land and fighters for the offenses on land and sea (offensive and defensive posture). If need be, build a sub or two for a cheap threat.
Note: Another possible idea is to produce an Industrial Complex at French- Indo-China-Burma or India to provide easier production of land troops on mainland. However, you must be careful that you do not lose this complex and so should attack India on the first turn.
Atlantic Theatre - if possible, send whatever sea power possible to the UK naval zone to provide defensive cover. If Germany has naval superiority, consider building transports (and infantry to fill them) to prepare for a initial strike at Africa, or Norway-Finland.
Pacific Theatre - retreat remains of pacific fleet to the continent and support with subs built this turn. Provide enough of a presence in the Pacific theatre to deter the Japanese from attacking North America.
Use whatever remaining funds to build up a respectable air force that can quickly respond to any Axis aggression in either theatre.
Despite the initial advantage that the Axis have at the beginning of the game, the sheer economic power of the combined Allied forces will quickly turn the tide to the Allies favor in 2-4 turns as long as Russia does not fall. Germany MUST increase it's economic output by taking over as much of Africa as possible, and prevent Russia from producing at Karelia.
Japan will be able to survive for much longer than the Germans as they have the only significant industrial complex in eastern Asia. They must help the Germans reduce the economic output of the Allied forces by conquering as much of Asia as possible.
The Allies will have to lose as little territory as possible as they build up their military strength. Once the United States becomes fully mobilized, it will be difficult for the Axis to stop the Allied onslaught.