I learned "My girl's a corker, she's a New Yorker" as a kid in Washington,D.C. with many of the words cited above. When I moved to New York City in 1956, they sang it as "There's where my money goes, to buy my baby clothes..."
My friend from the Ozarks sings, "She wears silk underwear, I wear my last year's pair." which I thought matched the phrase "that's where my money goes" better than any of the verses we sang as kids. She learned the song from a record (maybe Burl Ives?)
I looked in "The New Song Fest." They have the Vassar Hygiene Song followed by the parody of my girl's a corker with 14 college verses including those cited above (pages 54-55.)
We also learned "Marching to Pretoria" in school (probably in D.C. -more singing in the schools there.) The words are about doing things together, "as we march along."