What was the military significance of Africa? I mean, other then the British having it? Presumably the eventual invasion of Italy?
Reason one was the Suez canal. The Brits controlled Gibraltar so the Germans
couldn't had trouble get subs and couldn't get cruiser-raiders into the Mediterranean while the Italian fleet got smashed in the opening days of Italy's belligerency. That made the Suez canal a massively valuable asset. Convoys from India and Australia could save a lot of time by going to Suez instead of going round South Africa. On the other hand if the Germans controlled Suez, their sub attacks would have been way more effective.
Reason number two is that Iraq and Persia were great sources of oil. The Germans desperately, desperately wanted sources of oil besides Romania, which hit peak oil in 1943 IIRC. We often forget because the war was ending anyway, but the Germans completely ran out of oil by the end of the war. If not for the rapid shrinkage of their armed forces and the oil seized when Italy surrendered, the Germans would have run out of oil faster. The Germans were thus willing to gamble an awful lot on trying to get oil fields from Iraq or Baku.
This thread should cover things from Japanese-soviet N.A.P. (if the Japanese had invaded the USSR could the Russians have held up, and what resources did the Japanese have to spare at the time of the signing?)
Japan actually did run out of oil and had a ridiculously overstrained merchant marine throughout the war. They could have seized Vladistock but what would they have done after that, driven into Siberia and died of hypothermia when they ran out of oil to truck materials to the front? Yes, they would have tied up a few divisions that were historically transfered west and took part in the first Soviet winter offensive. But I suspect it wouldn't have made all that much difference on the German-Soviet front. I definitely don't think that would have been enough to tip the balance in the favor of the Germans.