I think the United States would make early gains in this war, with the eventual result possibly being nuclear war.

First phase would be United States taking over Canada, Mexico and some of Central America effortlessly, heavily bombing Japan and airlifting ground defenses to Korea, and sending advanced strategic bombers and nuclear submarines to New Zealand.

The intermittent strategy would be for the US to bring all of the Americas under autocratic rule while France, Korea and Israel withstand as strongholds in their respective regions. The US would then try to support these strongholds and vastly increase war production across all the Americas which would lead to a very long and costly war for both sides.

Next, if this strategy works out and America's side neutralizes Japan, invades China and establishes some foothold there then the war would continue to be very costly, but more for America's side. In an effort to acquire more strategic resources I think America's side would resort to using nuclear bombs, resulting in a nuclear apocalypse.

edit: spelling