Hunh, Blackadder maybe? Until at least that last episode. Or yeah, Hogan's Heroes would fit. I remember my mother, who grew up during WWII, being REALLY offended by Hogan's Heroes and forbidding me to watch it. (So of course I watched it.)

Dr Strangelove? Most of the ones I could think of are way older....Allo Allo, Dad's Army, McHale's Navy, how I Won the War, and then I ran out. (As said above, WII comedy was not a popular genre in my house growing up.) And a lot of the comedies seem in sort of sub-categories -- hapless hero with a bunch of nurses, or boot camp comedies, or civilians trying to make it on the Home Front.