Here's a set of records I've known for as long as I've known what a record was. Abe Burrows was a writer, humorist, radio performer, and much more (including being the father of James Burrows). In 1950 or so, he released a set of four 78's (and, apparently, a 10" 33 RPM album, too) under the title "Abe Burrows Sings?". My parents bought it shortly thereafter, and it was the sort of thing that received frequent plays (and frequent references to it in conversation) in our house.
If and when I come across this collection I will post a scan of the cover, but for now it's hidden somewhere amongst my parents' things in the basement. Some time ago, I made MP3 copies of all of these songs, though, and offer them here for your enjoyment.
I love all seven of these songs/skits (one being a two-parter) to varying degrees - "Boulder Dam" and "The Gypsy's Violin" are favorites. But there are great little jokes sprinkled throughout, really funny set pieces (particularly in the Boulder Dam record), and just a great, winning way with the whole presentation. I'd be surprised if these weren't a big influence on Tom Lehrer. (And at least a couple of these songs were reworked for use by the Muppets, a fact that I find fairly mind-boggling.)
Abe Burrows later released another 10" 33 RPM album, which featured a song called "The Girl with Three Blue Eyes", and which is also somewhere in that basement of mine. It's also got some fantastic material, which I'll share here when I come up with it.