Depends on what changed. Axis victory would have hinged on three possible outcomes:
- The United States staying out of the conflict (no Pearl Harbour assault, no German u-boat attacks on American vessels, and Hitler & Mussolini not declaring war on the USA in response to the US declaration of war on Japan.)
- Operation Barbarossa not happening.
- British defeat or withdrawal from the war.
In a scenario where the Japanese never attacked Pearl Harbour and never dragged the USA into the conflict, Hitler may have been able to eventually conquer Britain, turn his efforts towards Operation Barbarossa and take control of the entire European continent, along with parts of Asia. The Holocaust would likely have still happened, as the Final Solution was put in place six months prior to the Battle of Stalingrad, which turned the tide of the war in our current timeline.
Lack of US involvement leads to a scenario where nuclear weapons would not have been invented until much later, as Germany had not actually been working on weapons of mass destruction, and the Manhattan Project would never have occurred. World War III would likely have been fought between the Nazis/Japanese and Soviets, while the US would have remained isolationist.
A scenario where Operation Barbarossa never happens (neither Hitler nor Stalin attack each other) may be different. Hitler consolidates his European gains, never attacks the Soviet Union and focuses his efforts purely on the United States and Africa, securing many wins without his armies being stretched so thin. In that scenario, Jews are likely exiled to penal colonies established in Africa or the Middle East, from lands conquered from the British. The Holocaust may happen further down the line, but some historians think it was the unique wartime conditions on the Eastern Front that led to the Final Solution being considered - Nazi Germany actually tried resettling Jews in other lands prior to WW2.
British withdrawal (Hitler negotiating peace with Churchill) or defeat (Nazi Germany winning the Battle for Britain) may have led to Operation Barbarossa happening sooner, and with the Soviet Union not so far along in their industralization efforts, they would have likely lost Stalingrad, Petrograd and possibly Moscow. It either would have been a long and bloody war of attrition or a swift Soviet loss.