The 2011 Korean film "My Way" (Mai wei) is a true story about the Korean Yang Kyoungjong, who was first conscripted into the Japanese Imperial Army. I was captured by the Soviets and then joined the Red Army. Then he was conscripted into the German Wehrmacht, and finally captured by the Americans on D-Day. It is an amazing story.
There's another soldier who served in three armies. Lauri Törni served Finland, Nazi Germany and USA although he served USA in the Vietnam War under the name Larry Thorne.