Was Lee Harvey Oswald in the war?

Which war?

If you are referring to World War II, he was not. By the end of that war, he would have been only 6 years old.

If you are referring to the Korean War, he was not either. By the end of that war he would have been a mere 14 years old.

Besides WWII and Korea, there is no other war that America fully participated in during his lifetime, as he himself was shot an killed in the year 1963 by Jack Ruby.