The 'Eastern Crusade' is meant to represent a possible response by Germany to an extension of the Maginot Line in the 1930s. It's the most radical of the alternative history options in the scenario.
The theory is that, faced with a France effectively walling itself off from the rest of the Continent, the Central European and Balkan Powers are forced to ally with Germany. Bulgaria, Hungary, Rumania and the Croats and Slovaks eventually did, of course. The EC option assumes that Hitler was also able to pressure Poland and the Baltic States into an anti-Bolshevik alliance, with a view to invading the USSR before moving against the West.
To stop waffling and answer your question:
Axis benefits -
The 'Allied' Polish units are withdrawn and replaced by similarly sized 'Axis' Poles
The Baltic States mobilise as pro-Axis Allies and will no longer disband when (if?) France falls
Rumania and Hungary will mobilise as pro-Axis Allies (Rumanians get an extra mobile corps, assumed to be extra German equipment)
Finland (50%) and Bulgaria (25%) may mobilise as pro-Axis Allies
The Western Allies are not able to declare war on Germany until 25 - 55 turns into the war (25% chance after 25 turns, rising to 100% after 55)
The German reinforcements usually triggered later by the Russo-German War start to come on
The 25% chance of Belgium joining the Western Allies disappears.
Allied benefits -
The USSR gets four 'Red Cavalry' Armies, each of one HQ and two '3 - 4' cavalry corps
The Stalin Line is extended by 20 more '2 - 5' static units along the existing fortified areas (i.e. wily old Uncle Joe sees it coming in the 1930s)
The - eventually massive - Russian reinforcements usually triggered later by the Russo-German War start to come on
The Maginot Line is extended all the way to the North Sea/Channel
Other things to bear in mind -
The Germans still have the 'Barbarossa' bonus
Iran may (75% chance) join the Germans after about two months
The fierce winter of 1939 will still stop ALL combat as usual between turns 24 - 37 (slight variable): this may allow the USSR to regroup
I think that's most of it. It will be nothing like what really happened in WWII, but it can be an interesting alternative. There's no point triggering the Eastern Crusade if you don't fancy this sort of game.
The alternative is to move West as usual (you'll still need to knock out the pro-Allied Poles first) and be prepared for a tough slog against the improved Maginot Line, although it isn't invunerable. Maybe a move through Switzerland or Italy, which aren't covered by the Line, or more naval landings in the Channel ports?
Most players agree in advance whether they want to play an Eastern Crusade game, in which case the Allied Player extends the Maginot Line in agreement with the Axis Player.