The frying pan guy is Ol' Dan Tucker. There are many variants of the words, but I learned some of it like this: "Went to town the other night to hear a noise and see a fight; all the people gathered round, singing, 'Ol' Dan Tucker's a-comin' to town. Say, get outta the way for ol' Dan Tucker - too late to get his supper. Supper's over an dinner's cookin' - ol' Dan Tucker just stood there lookin'." ... "Ol' Dan Tucker's a fine ol' man - washed his face in a frying pan - combed his hair with a wagon wheel - died of a toothache in his heel."
You might want to look for some of the recordings of Burl Ives. There are compilations on some CDs. You'll find a number of these old songs because they started out as folk songs, not children's songs. It's the way I learned many of them when I was a kid. Happily, I didn't understand what all of the songs were about - so the romance-death-and-violence stuff (not to mention tying the goat to the railroad tracks) in the songs didn't get to me; I just thought it was all silly.
One I particularly loved was called "The Big Rock Candy Mountain." I thought it was just a kid fantasy song, and had no idea it was a hobo song until I grew up! I still like to sing it.
Another source might be Laura-Ingalls-Wilder.com - because the music from the Little House Books is being recorded, and you might find some of the old songs you're trying to remember.
I know a poem about a crooked man, but I don't know music to it: "There was a crooked man who walked a crooked mile; he find a crooked sixpence upon a crooked stile [steps built across a pasture fence]; he bought a crooked cat who caught a crooked mouse, and they all lived together in a little crooked house." That's an old nursery rhyme.
Do you know the song about the old lady who swallowed a fly?