When the United States entered the war in December of 1941, the war in Europe was going very badly for the Allies. The war in the Pacific had pretty much just started, but it was not going well either.
In Europe, Germany had conquered essentially all of Europe. There were a few countries on the continent that were neutral, but none left that were hostile to Germany except for the USSR. And at that point, the German army was occupying most of the European part of the USSR.
So, at the time the US entered the war, things looked very bad for the allies.
As for how the war was won, you've asked some questions (like about the strategy) that answer that.
World War II was a long drawn out war, fought between countries coalition of more than 50 countries including the most powerful countries of that time, and extending over three major continents. In a war like this it is not possible to speak of just one unchanging foreign policy. In a dynamic situation like a world war is necessary to have a flexible foreign policy in line with changing situation.
For example, initially the policy of USA was to not to participate in the war only selling war material for cash to allied country. This was changed to the policy of supply on lend-lease basis. Subsequently USA decided to to participate in the war directly.
Similarly take the case of Russia. Initially it did not oppose the actions of Germany, but was forced in to the war nearly one and half year after the start of war. In situation like this foreign policy of any country toward Russia could not have remained same throughout the war.
Similarly, Bombing of Pearl Harbour by Japan in December 1941, made a shift in foreign policies of all the countries, towards Japan in particular and towards the war in general, absolutely essential.
Coming to the question of how Allies won the war, to me the most important factor appears to be the greater combined military and economic strength of the allied countries.