I can't see three strong forces surviving. The struggle between Naziism and Communism was ideological in extremis.
The most likely for this scenario would be a "Fatherland" type situation with an ongoing conflict but stalemated somewhere near the Urals.
Instead of a "World War" we'd have a series of diverse conflicts and for that to happen there has to be no Japanese attack on the United States. Instead, Imperial Japan is bogged down fighting Communist forces in China - the Red Chinese are in ideological alliance with Soviet Russia and they form the Comintern but there's little practical help each can give the other. Meanwhile, apart from fighting the Japanese, the Chinese Communists are fighting the American-backed Nationalist Government in Chungking whose own efforts against the Japanese have been largely ineffectual.
In Europe, Germany dominates the Continent but Britain, in alliance with the United States though the latter is not a belligerent, remains. There is an uneasy peace in Europe but the British and Germans (and their allies) battle in the Middle East and North Africa. The Americans supply money and materiel aid but that's all and on a strictly commercial basis. German-American relations are frosty and the Germans are active seeking to destabilise Latin America but there is no war.
In the Far East, the Japanese support liberation movements in Indochina and elsewhere but the large British and American naval presence in the western Pacific has so far deterred Tokyo from action. There is a nominal alliance between Germany, Japan and Italy but it is more symbolic than actual.
Fast forward to 2000 (let's say) - the United States and Britain form the core of a democratic capitalist alliance which includes the former Dominions of Canada, India, Australia and New Zealand along with South Africa and some of the Latin American states. The German Empire comprises Europe except the British Isles, much of North Africa and the west of the former USSR - Spain and Portugal are in the Empire as are parts of Africa and Persia. It is in alliance with Japan which controls Indo China and Thailand (though not directly). Finally, we have the Communist Bloc of Russia and China which has a large land area.
I suppose I could call them Oceania, Eurasia and Eastasia but I think that's been done.
