Some more of me notes ...

Girl I Left Behind Me
The oldest text is from issue 72 of "Charms of Melody" (approximately 1805-6). However, in a songbook, "The New Whim of the Night, or the Town and Country Songster for 1799", is a song "The Girls we love so dearly" 'Written by R. Rusted - tune "The Girl I left behind me".

Wm. Chappell in "Popular Music of the Olden Time" had said quite a lot about "The girl I left behind me" being connected with "Brighton Camp" and being an 18th century song, though he gives no solid information to demonstrate an 18th century date.

James J. Fuld, "The Book of World Famous Music", notes that the song appears in Bell's "Rhymes of the Northern Bards", 1812 and points out that "Brighton Camp Quick March", 1792, is not the same tune. The tune appears as "Brighton Camp or the Girl I Left Behind Me" in Riley's Flute Melodies (1816).

Hallelujah, I'm A Bum
George Milburn, in his Hobo's Hornbook says that a version of this famous hobo song "was found scribbled on the wall of a Kansas City jail where an old hobo known as One-Finger Ellis had spend the night, recovering from a overdose of rotgut whisky". Al Jolson made a big pop hit out of this. In England, though, "bum" means something else, so over here he had to sing: Hallelujah, I'm a Tramp.

It Was A Lover And His Lass
A late 16th Century English Lute Ayre by Thomas Morley. This song is sung in Shakespeare's "As you like it" which was first performed in 1599 or 1600. The use of the phrase "pretty ring time" appeals to my sense of humour. This is because, whilst most people are aware that Saturn has rings, in the Cambridgeshire fens it is more to do with Uranus.

The Newry Highwayman
BruceO provides some information in this thread. The song is also called "Wild and Wicked Youth", "Rambling Boy", "Irish Robber". Versions are set in England and in Ireland, but there is no single common title.

:-)