What strategy did the Allies use to defeat Japan?
I am not so sure it was a strategy as much as the enforcement through the use of a weapon that was far more powerful that any weapon that had ever been used. The United States dropped atomic bombs on Hiroshima and Nagasaki.
The decision had not been an easy one, but so many soldiers were dying in combat and the agreement was that the bombs use would do more harm than good. The Allies were in agreement that it would bring a quick end to the war. It did what it was supposed to do, but unfortunately many people in Japan suffered for many years due to radiation exposure and their rates of birth defects in the area was extremely high.
My history class just went over this last week :)
Since naval confrontation with Japanese war ships proved to be too costly for the US and its allies, they eventually resorted with aerial assults on enemy ships. Ofcourse, the Japanese had their kamikaze planes to take out destroyers or aircraft carriers. It was primarily that reason the campaign in the Pacific led to mostly bombing Japanese ships while US destroyers would go after Japanese subs.
In 1946, when Truman came into office, even he wasn't aware of the atomic bombs production nor was he sure they would even work. But in his decision to end the war, he gave the go ahead to bomb Hiroshima and Nagasaki. Air strike was the way to go since the Japanese had bigger and better guns than the Allies.