It is very hard to generalize for "the people of the US and allied nations and all the soldiers" — these are huge groups.

But the general response was a mixture of excitement and elation (they looked like the end of the war), and dread (what kind of new world had been entered into — what would the future hold?). Some countries and individuals condemned the bombings as inhumane, some (including in the US military) would later claim they were unnecessary to win the war. On the whole though, they were "sold" as being used to save lives and end the war, and since the lives that were lost were (mostly) Japanese, most Americans and members of Allied nations were OK with that idea. But there were also strong calls for international efforts to end the threat of nuclear weapons permanently, by using treaties developed in the United Nations, and avoid arms races and the possibility of future nuclear war. Obviously these failed.