This was a fascinating thread (which I found searching for "She wears my BVDs, I stand outside and freeze, Yes boys that's where my money goes", which my dad sang for me in the 60's).

It's pretty clear that there are four different songs here. (Not that hard to tell if you check scansion and lyrics and do some YouTube searches)

1) "My Gal's a Corker" - waltz, written by John Stromberg in the late 1800's

2) "My Gal's a Corker" - rag, possibly written by Ray Valdes in 1941; perhaps filking an existing tune. This is a completely different song than #1, with different lyrics and meter, but shares the same title. It had traveled to Scotland by the mid 1950's to be recorded by Alan Lomax (http://www.allmusic.com/album/singing-in-the-streets-scottish-childrens-songs-mw0000655458)

3) "Vassar Hygiene Song" - shares a few lyrics with #2, but clearly a different song.

4) "Nobody's business what i do" - blues song that has a similar meter to #2 but different tune.