Here is a list of the song recordings (version/parody notes are Gifford's):

Jam on Gerry's Rock
The Wexford Girl
Johnny German
Miller's Will
My Brother John
I Met the Old Lady One Morning (version of "Dick Darby, the Cobbler")
I'd Married a Dandy Just Nineteen Years Old
I Once Did Know Farmer
Paper of Pins
Mister Captain, Stop the Ship
There's a Pine Tree on the Hill (parody of "Little Log Cabin in the Lane")
There Was an Old Lady Lived over the Hill
We're Just Plain Folk
My Mother was a Lady
Irishman's Shanty

    Bawdy songs:

The Sea Crab
My Name is John Williams
Chisholm Trail
Darby Town
This Way and That Way (note: this version is in the DT, SongID=7282)
Peddler and Joe
There Was a Little Bird
Did You Ever See Sally Make Water?
I Dreamt Last Night
I Fucked an Old Lady (two versions)
I Went Upstairs to Get a Glass of Cider
Monroe is a Beautiful Creature
Oh, Sally, Come Quick
Old Lady She Shit in the Haymow
Old Lady in the Haymow
Old Mother Hubbard
Rory O'More
Said the Little Red Rooster to the Little Red Hen
She Jumped in the Bed
Up Jumped Sally with Her Feet upon the Drum
Oh, She Set with Her Feet Cocked up on a Drum
Yankee Doodle Had a Cat
Oh, Baker, Oh, Baker, He was a Shoemaker
I Stuck My Nose in a Billy Goat's Ass
There's a Pretty Spot on Nellie
Was a Rink in My Dink
My Name is Bob Taylor

   Recitations and a Joke

Here's to the Girl Out West
The Indian and the Druggist
I'm Hunt de Skunk
Dangerous Dan McGrew (a parody of the original Robert Service poem)
Down in the Lehigh Valley