I mean, like, "A Modest Proposal"—putting up helpless little Irish babies for retail sale as comestibles?—eeeeuuww! Some people may think that cannibalism is funny, but I don't. There are things you just don't joke about.
FWIW, I regard Strangelove as one of the greats. I suspect that your own appreciation was hampered both by the cultural once-remove and, much more, by the forty years of dense history separating your viewing it for the first time in 2004 from the audiences at its original release.
cordially,