O'Neill's books were all published in early 20th century; "1850" refers to the number of tunes rather than the date.

It is generally accepted that Union Army bandmaster Patrick Gilmore wrote (under the pseudonym of "Louis Lambert") both the words and music to "When Johnny Comes Marching Home."

At some point, Gilmore claimed that he'd learned the tune from a black singer in New Orleans. Irwin Silber suggests that the tune could have been that of "The Crawdad Song," which Gilmore revised into the minor mode.

Most American versions of the Child Ballad of "The Three Ravens" are rather surprisingly sung to Gilmore's tune, so maybe they came first.
There is a hint of musical resemblance in the opening bars of Frank Kidson's English version of the raven song, which his informant claimed to have learned around 1830, IIRC.

The belief that "Johnny I Hardly Knew Ye" predates "When Johnny" is poorly supported. Known Irish printings of the former stem from after the American Civil War. Its reference to the "Island of Sulloon," evidently Ceylon (Sri Lanka) (where British troops fought in 1802) is of no probative value as to the date of the song's origin. Furthermore, the melody printed with the formal sheet-music edition of "Hardly Knew Ye" (ca.1869) is NOT the familiar Gilmore tune!

The "John Anderson" tune, however, is both authentically 18th century AND close enough to "When Johnny" to have provided Gilmore with possibly unconscious inspiration. The same may be said of "When Johnny" vis-a-vis the post-WWII hit, "Ghost Riders in the Sky."