I was bored and did some thinking about the setting. Naturally, I've got a bunch of ideas, accounting for the setting as described with some extrapolation. Warning: Long.
A wire went untapped, an informant went misplaced, and a transmission went unheard. The Japanese attack on Pearl Harbor was the surprise Admiral Yamamoto hoped it would be, and three American aircraft carriers were rendered inoperable. Denied the fulcrum of it's power in the Pacific, the American military battled the Japanese navy to a stalemate, it's great industrial advantage outmatched by Japanese preparation and courage.
Meanwhile, the strong personalities within Hitler's inner circle managed to usurp Der Furher's will, and convinced him that fighting across the English Channel, conquering the Algerian desert, saving Moussolini's butt in Greece, and invading Russia all at the same time would be problematic to say the least. Instead, the Afrika Korps systematically ousted the beleaguered British contingent from Egypt and Palestine (the later with particular relish).
America was forced to commit more of it's economic strength to a still unsuccessful campaign against Japan, and was less able to aid Britain in tackling Germany. Combined with the stronger German presence in Africa, a long-route invasion of Europe via the Mediterranean and Italy looked even harder. After several ultimately ineffective attempts at landing a foothold on the continent, pressure got the better of judgment, and Allied command resolved to go for broke with a full scale invasion of northern France in mid-1943. It was a bloody disaster.
Back in 1941, Operation Barbarossa proceeded right on (that is, off) schedule, and stalled on the Volga river and the gates of Moscow, before the largest counter-offensive in history steamrolled all the way back into Belarus. Without the fruitless expenditures of the Battle of Berlin and defending against Operations Torch and Husky, a consolidated Nazi Germany was better able to defend itself. Germany's saving grace was the elimination of Hitler. No longer committed to his insane schemes, the Kreisau Circle redoubled the defenses of the Eastern Front, with all experimental development devoted to the one wonder weapon that might work.
On October 28, 1944, a German rocket plane dropped the world's first functional atomic bomb on the Russian forces advancing through Lvov, and changed the world. Nazi Germany's sue for peace with the Allied forces finally had the weight it needed, and the Western front went silent. America developed it's own nuclear explosive the next Spring, and resolved to frighten the Japanese into an armistice. Japanese spies had learned of the plan, if not the weapon itself, and fired off their gift from a desperate Germany at the same battle, coincidentally launching the only nuclear exchange in history over the island of Palau on March 17, 1945. Not knowing each other's full capabilities, the Pacific war quickly came to an unofficial halt.
The Allies scrambled to build a position for themselves in the new atomic world. Left bankrupt with no victor's guilt, Britain tightened it's control of it's many remaining colonies, with so much American assistance they could hardly be called Britain's anymore. The exhausted but vindicated Axis went to work fortifying itself against any possibility of a renewed assault. Japan's conquest of eastern Asia slowed but did not stop, seeking any gains after the devastating war with America. The Soviets fumed but accepted the obvious, and the advance across Europe turned to a consolidation. It would be another five years before the Soviet Union could demonstrate it's own nuclear bomb, by which time any thought of reopened hostility would be suicide.