> how were slaves a major part of Nazi war effort or economy?
The Nazis employed slave labor on a massive scale. Their slaves were Jewish prisoners, political prisoners, and POWs.
The US free labor produced plenty of war material for two major wars, and enough left over to supply Britain and the Soviet Union. US troops were well fed, with plenty of gas, bullets, airplanes, ships, aircraft carriers, medical supplies, trucks, everything, and also managed to ship it all to the war zones.
The Nazis and the Japanese never had a chance once the US got going. They had critical shortages of everything.
For example, what did the Nazis do when the battleship Bismarck was sunk? Game over for the Kriegsmarine except for the U-boots. What did the US do when the Japanese wrecked the US aircraft carriers? Built lots more! What did the Japanese do when their carriers were sunk? Game over for naval aviation.
Also, the Wehrmacht in WW2 was still very much a horse driven army. The German propaganda newsreels, shown endlessly in WW2 documentaries, avoided showing the horses and loved showing the mechanized troops. I don't think the US used any horses at all.
Free labor also sunk the Confederacy. The Confederacy was never able to properly supply their troops with guns, cannons, powder, food, uniforms, or even shoes. They were largely barefoot.