If it happens, its a whole new war. Its not WW2 any longer, it the Great Eurasian Conflict. The Japanese are in OTL getting their asses kicked by Zhukov. If the Soviets and Germans fight on the same side, then the German declare war on Japan, the Japanese ask the British and the Americans for help and we have a situations that bears little resemblance to the OTL war.
This is I think this the start of a really interesting scenario.
Russian preoccupation with an offensive into Western Asia might very well lead to the Northern Faction coming out on top in the Japanese political power struggle. If so they could seek to hit the Russians in the Far East and get revenge for Kalkhin Gol, and get aid from the British. (The difficulty here would be that the Allies would very much look like the losing side and the Japanese might not want to tie themselves to a seemingly sinking ship)
A renewed Anglo-Japnese alliance would have major difficulties in the shape of Japanese ambitions in China, but the British by this point might be so hard pressed by the Soviets in Afganistan and Iran that they could overlook it, especially if these Chinese nationalist and communists form a united front at the behest of thier German and Soviet benefactors, more firmly fixing themselves as part of the opposition.
realistically lying for much of the war the Axis and USSR are going to be winning hard in pretty much every theatre due to British overstretch. However I think the back stab in inevitable. Once British forces retreat across the channel and the Luftwaffe starts the Battle of Britain, I think Hitler will begin considering the British as a contained threat and will move his ficus onto preparing for Barbarossa.
Similarly I think Stalin will be preparing to betray Hitler from an early stage. Perhaps the entire Soviet southern offensive will be directed at seizing the British controlled oil production, before Britain capitulates and it falls into German hands.
The betrayal probably happens a little later than in OTL but from then on I think enough hostility will have been fostered between the allies and both belligerents that no offer of cooperation is considered for either the Germans or the Soviets.
Instead a three way global war develops that gives the Allies the breathing room they need to begin making up ground.
When the Americans get involved will be significant, and probably later. With no direct attack like pearl harbour, I think it will be predicated on attack on US shipping. The combined Soviet and German raiding fleets in the North Atlantic will present a significant problem.
Regardless of when they enter the Americans are likely going to have significantly more issue with Japan than the British do and will likely refuse to get involved in the Far Eastern theatre or send direct aid to Japan.
American Expditionary Forces will probably make an appearance in Iran and Western India first and an invasion of Europe later on. American lend lease will probably be routed from Australia to Japan to at least give a modicum of separation. The British might try and stipulate that this material is to be used against the Soviets, but the Japanese will likely flout that.
Eventually as the Germans and Soviets hammer each other across Eastern Europe the allies will make an American lead invasion of Europe and begin advancing eastwards. The Germans now pressed on two fronts and ha,meted by strategic bombing will eventually fold. In this TL you might even see large parts of the Western German army surrender and defect to the Allies on the condition they be allowed to fight under Allied command to fight a Soviet invasion of Germany.
The end of the war will likely se Germany occupied solely by an allied military commissions and The USSR forced into surrender by a nuclear bombing campaign. No occupation of Russia is practical however, and so instead the soviets are disarmed and forced into large territorial concessions, likely including Ukraine, Karelia, Central Asia, the Caucaus, and the Baltics. The Russian Far East probably becomes a protectorate of Japan as part of the co-prosperity sphere. Likely with much of the Russian population removed by population transfers.
The post war world then features a shattered and exhausted Europe reliant on American economic aid, an expansive Japanese empire and system of client states in Asia, a slowly disintegrating British Empire, and a beaten but not broken Russian rump state that thirsts for revenge.
