How can I beat Germany in Axis & Allies: Europe?
The dynamics of the game are based on the following: 


In "real life," Germany would have beaten Britain and Russia if the latter two did not receive American help. 
Overwhelming American power (almost that of Britain, Germany and Russia put together) meant that the Allies would be heavy favorites once America joined the war. 
In the game, America has a fraction of its "real life" power, enough to make the Allies favorites, but not enough to make them prohibitively so. 


In the game, if Germany conquers Russia, Germany-Russia is stronger than U.S.-Britain, which was not true in real life. Therefore the game imperatives are 


for the Russian player to successfully defend Moskva against capture 
For the Americans to find a way to make their weight felt.


Russia needs to play strict defense, with the ultimate aim of defending Moskva. That doesn't mean that they should neglect the surrounding territories (that would make it too easy for the Germans to capture the extra "income"), but rather to beat a "fighting retreat" as in real life. That is, they should mostly build infantry, and use them to defend territories in a die-hard fashion, and leaving air and armor units in Moskva for "strafing" counter attacks, extracting the highest possible price in time and firepower for territories lost. 

The Americans need to find a way to help the Russians, making effective use of their margin of superiority. One way is "Lend Lease," sending e.g. fighter units to Moskva for its defense, so that the Russians can build "all infantry."  That is a genuine, but inefficient use of American resources. The second way is to launch "bleeding" attacks in Europe 


Scandinavia, which threatens to open a direct route to Russia or 
France or Italy, which directly threatens Germany, or even 
North Africa, which reduces German income from the south. 


If these initiatives are successful, the Germans will have too few troops/income left to defeat Russia.

The Allies CAN lose if the die rolls are bad. Barring this, they have a sufficient margin of superiority to win if they play as well as the Germans.