I've played Axis & Allies quite a lot. Its generally held that the game as it stands is rather heavily balanced against the Axis. The reason?

On turn one, a light attack by the Russians against Eastern Europe virtually destroys any chance for a significant German offensive on turn one. Don't waste too many tanks here. Use your fighters for offensive punch and use the infantry to absorb hits. Withdraw the fighters to Karelia and leave your infantry as a garrison in Eastern Europe. Building infantry almost exclusively and placing them in Karelia normally means that Russia and Germany will trade Eastern Europe back and forth for a turn or two. While this is happening, the other Allies are building an armada in British waters for the invasion of Germany. This scenario means that for the Axis to win, Japan must move swiftly against Russia in the east. This isn't easy because of the difficulty of sending overwhelming force across the Sea of Japan (plus there's all that territory to conquer before they get to Moscow!).

A house rule that is often used to balance the game is to forbid Russia to make any attacks on the first turn. They are allowed to buy units, make-noncombat moves, and deploy the new units. This normally means a pile of infantry is placed in Karelia on turn one to defend that critical industrial complex. Unless the Germans concentrate the Luftwaffe solely on taking Karelia it will probably stand (or at least trade hands) for a turn or two. Concentrating the Luftwaffe here means Germany is likely ignoring the threat from the British and Americans...normally a bad idea. A German attack on the Caucasus is generally a bad idea because it exposes their "supply lines" to attack from Russia out of Karelia.

My strategic objectives for the powers is thus:

Russia: Hold out against Germany and apply economy of force tactics in the east to delay the Japanese. Buy lots of infantry.

Germany: Use the Luftwaffe to hamper Allied shipping in the Atlantic. Maintain heavy pressure on the Russians, but don't expose too much armor to counterattack. Drive on Moscow first.

British: Cooperate closely with the Americans to build up a large, well-defended fleet in the Atlantic. Bomb Germany strategically. Perhaps try to get a foothold on the continent at Finland-Norway.

Japanese: Neutralize the Americans in the Pacific. Concentrate land forces in Asia for a drive on Moscow.

Americans: Work closely with the British to build up a large, well-defended fleet in the Atlantic. Reinforce any footholds the British gain on the continent.