The era animators and other filmmakers love, an era of gentility, straw hats, handlebar mustaches, and ragtime piano. This is the era Disneyland's Main Street USA takes place in, though more recently that has been expanded to a broader "old-timey" era, with '00s-'20s and a little bit of '30s, as well as more recent throwbacks (you'll hear songs from The Music Man playing among the authentic tunes). Disney's lack of research shows through again as a few of these songs aren't even from the 1890s.
The third act begins with "She May Be Somebody's Mother", written by William C. Carleton, which is all that I could find out about it.
"The Bowery", music by Percy Gaunt, words by Charles H. Hoyt, part of the Broadway play A Trip to Chinatown.
Don't worry, it's in there somewhere.
"After the Ball", written by Charles K. Harris in 1891, and one of the first songs to become a million-seller.
"Down in the Licensed Saloon", written by W.A. Williams in 1892, and apparently a take-off of the extremely similar "Where is My Wandering Boy Tonight?" by Rev. Robert Lowry. There is also "(Bring Back My) Wandering Boy" a folk song based off of "Somebody's Boy is Homeless Tonight" by R.S. Hanna.
...I think. It's all so confusing I'm not sure I'll be able to find the one Disney used (W.A. Williams).
Alternate lyrics: http://firstname.lastname@example.org?SongID=10336
"(Won't You Come Home) Bill Bailey", written by Hughie Cannon in 1902.
Notably adapted into "Bill Spacely" in the Jetsons episode "Miss Solar System":
"Sweet Adeline", words by Richard H. Gerard, music by Harry Armstrong, 1903. Very popular with animators, and for some reason almost always performed drunk (or at least queerly). It's unfortunately hard to find straight renditions...
"The Old Grey Mare", a folk song that has become synonymous with horses in animation scores.
"A Bird in a Gilded Cage", music by Harry von Tilzer, words by Arthur J. Lamb, 1900.
"Ta-ra-ra Boom-de-ay", attributed to Henry J. Sayers, 1891, the next year given new words by Richard Morton. Also known as the melody for "It's Howdy Doody Time".
By the way, as an aside, if you've ever wondered if the Dilly Sisters ever did anything else... well:
Next up is "Modern Times", which wasn't a very descriptive name at all, as you'll soon see...