This is going to turn very nasty. There's no guarantee that the allies will defeat Stalin, and their war aims will be very different. Goering might simply agree to all war aims proposed with no intention of ever following through, so you could see a reverse postwar in which German troops stay in place throughout Eastern Europe and fascist client regimes are set up, territories are 'adjusted' and German holdings regained. The really scary thing is that it could work.
Japan might just be willing to join in the fun if it is promised Soviet territory in Siberia. It's not like they would be a very effective belligerent on land, but it's probably good to have them close the Eastern ports (easy enough for the IJN) and keep up a threat to prevent troops moved out of the Eastern provinces.
The USA, without provocation, might just stay out of this mess completely. Nobody will shed a tear for the USSR, and neither Japan nor Nazi Germany have enough support to trigger US intervention. France and Britain would be co-belligerents more than allies and would be able to fight this war at a greater remove, probably also with a bigger profit, but will end up facing a much strengthened Germany at the end of it.
Four-way cold war? Britain and France cast themselves as defenders of freedom against the Nazi menace that has swallowed up all of Eastern Europe, but cling to their colonial empires to support their military might while the USA urges them to let them go, but is unwilling to commit itself to a European war if the Germans cross the Rhine. Japan absorbs it East Asian gains and foments rebellion among the colonies, still fighting to crush China while hypocriotically demanding only Asians be allowed to oppress Asians. The United States are most concerned about the Pacific flank. Rump Russia is slowly restoring its military power and begins planning for a rematch.
Goering is likely to be a lot like Franco, though a lot more destructive. He doesn't share hitler's genocidal madness, but he does have a megalomaniac streak and would just love to play 'Risk' with live pieces.