OK, here are my answers to the quiz. Some of the answers given above, although different, are just as good.

1. Our Saviour, Christ, and His Lady. I SAW THREE SHIPS
2. On the DARK OLD WATERS, all alone. (Gordon Bok)
3. Gold I will give you and my daughter for your bride. THE GOLDEN VANITY
4. That's only a milk cow my granny sent to me. FIVE NIGHTS DRUNK.
5. After you've been havin' steak for a long time, beans, BEANS TASTE FINE. (Shel Silverstein)
6. MY GET UP AND GO HAS GOT UP AND WENT. (Pete Seeger)
7. A little bit of cucum, cucum, cucum, LITTLE BIT OF CUCUMBER. (a music hall song)
8. Oh, no, my love. Farewell! PLEASANT AND DELIGHTFUL
9. Pulled a great big fish out the bottom of the pond. FISHIN' BLUES (Taj Mahal)
10. Either "The Southern Pacific and the Santa Fe" or "A glass of water and a cup of tea" JAY GOULD'S DAUGHTER
11. 'Tis the bag he puts his provender in. TROOPER WATERING HIS NAGG (from "Pills to Purge Melancholy")
12. Bacon and beans, a bellyful. OH SHEPHERD, OH SHEPHERD
13. Sit on the bank and watch the crawdads die. CRAWDAD
14. When I grow rich (say the bells of Shoreditch). ORANGES AND LEMONS 2
15. I don't know when, but we'll get together then. CAT'S IN THE CRADLE (Harry Chapin)
16. IN THE PINES, in the pines, where the sun never shines. (Lead Belly)
17. Young girls picked them, ev'ry one. WHERE HAVE ALL THE FLOWERS GONE (Pete Seeger)
18. In the woods, dear mother. HENRY MY SON
19. Down in yonder green field. THE THREE RAVENS
20. Radio said, they are just DEPORTEES. (Woody Guthrie)
21. Mama will glove my hand. DON'T LET YOUR DEAL GO DOWN (and others)
22. With a straw, dear Henry. THERE'S A HOLE IN THE BUCKET
23. BONEY FINGERS (Renee Armand and Hoyt Axton)
24. Another day older and deeper in debt. SIXTEEN TONS