above all, the song/poem/limerick must be well-constructed to be a first class bawdy song. If you define, say, 5 classes, I will almost NEVER do one in class 4 or 5, as these are ususally just poorly done excuses to be smarmy and crude. (5th grade humor, I call it).Using 'vulgar words of language', as Woody put it, 'can' be done with wit and cleverness, but it takes careful writing to make them work well.....and, when it is done, it takes awareness & ummmmmm.....'sensitivity' to decide when & where to sing it.
I know a parody to "King of the Road", written by two friends of mine, that is clever, mostly well constructed, but has SO much to offend in it, that I have only sung it in public maybe 3 times.
Likewise the classic, "Charlotte the Harlot", which, in 'polished' versions has some of the funniest images and lines, but has poorly done versions that are awkward and stupid.
In my opinion, limericks are the surpreme form of 'sung' poetry which can make crude language funny...in the right context and presentation.