Confined to their own territory, the Nazis hopefully won't perform anywhere near the same atrocities as in OTL (remember, the Holocaust essentially started with Barbarossa). Poland will still suffer worse than ever, but I guess hopes are there won't be the same kind of organised, massive genocide (if/when Germany makes peace, they might have to take things like foreign opinion into account).
Between the Soviets and Japan, they'll set China's development back a decade or two. And with rigid Stalinism the mode of Communism there as well, China won't grow to challenge the West anywhere as fast as OTL. If a peace is negotiated, Japan will remain militarist and contrary, so the same could go for them (if invaded, they'd be crushed, though that's unlikely; the Sovs didn't have the resources for it).
The ME will be dominated by the Soviets, and perhaps also Italy and Germany; they can likely split it somehow, say, Italy get Saudi Arabia and the Sovs Iran/Iraq. Vichy France might get to keep Syria, though that'll be a liability rather than an asset in the long term.
(Strange scenario: might the Axis actually support the Zionist movement and set up an Israel? IIRC, Hitler primarily wanted the Jews out of Europe, whether they were killed or thrown out. However, these views gradually changed with the coming of the war.)
The British Empire would have to make peace, inevitably; with Japan neutralised and a very strong Axis coalition, the USA likely wouldn't enter the war. FDR will support Britain - and perhaps also, then very grudgingly, Japan - financially, but it wouldn't be enough. In the end, with Churchill at the helm, the end result would likely be the same - the visible end of Britain as a Great Power.
Now comes the question: would the Axis allow decolonisation, or would they prop up/supplant Britain's hold in Africa? Is it conceivable the Brits may sell off their colonies?