For the Korean War, Oscar Brand has an album of Air Force Songs that may give you an idea. The afore-mentioned "Itazukie Tower" is on it, as well as several others, many with origins in WWII. I liked "Cigareets and Saki and Wild, Wild Josies," a straight-forward take-off on "Chigareets and Whiskey." I'd like to hear what the Viet Nam vets were singing, but I suspect that they were mostly contented with top 40 radio stuff more than the more traditional "hanging around a piano in a bar" type singing of their forebearers.

Come to think of it, isn't there a whole series of links in the Mudcat links section that deals with Viet Nam?