I can speak only of my own family's experience during that war. My Grandfather was an Army surgeon in the Pacific Theater. I had almost no knowledge of what he did and saw in that war until after he died, when I read his diary of the war, as while he was alive, he never once spoke of it to me or even to my father that I know of.
He, along with many, many other soldiers in both theaters, saw and did things that were both horrible and seemingly impossible. To come home from such death and destruction to a country with a thriving economy, no war damage or experience, and massive celebrations treating them as heroes (rightfully so), I think it was very difficult for many veterans to adjust. They couldn't reconcile what they had experienced at war with life at home, so they simply buried it. I have heard that from many other historians as well, that soldiers came home from the war and never talked about it again. Some until their deaths, but many until much, much later in life. I think that's because there were no words to explain it to those of us that hadn't experienced it. At least, no easy ones.
It is very difficult to generalize about such a huge topic since there were millions of soldiers of the various nations and their experiences would often have been very different.
Of course, the greatest impact was on soldiers who were killed or badly wounded. Those soldiers had their lives ended or changed forever. Another major impact was on those soldiers who saw friends die and who were exposed to death on a regular basis. This sort of experience caused many of them to experience post traumatic stress disorders later in life.
To some soldiers, the war was an opportunity to broaden horizons. They would have met people from different areas of the US and they would have seen places that were totally unfamiliar. These experiences would have made them much more aware of the world than they previously had been.