The narrator "shags" landlord or bartender O'Reilly's daughter, then assaults father, mother or both.
Annotator Legman (pp. 138-139) includes the text of "The Rover," which he dates to 1790, as the forerunner of the modern bawdy ballad. The "C" text in Randolph-Legman I is only coincidentally "One-Eyed Reilly." - EC
This exists in an extremely bowdlerized version [in which the singer wants to "marry" rather than "shag" the daughter, and in which the daughter is the only one to receive his attentions], which was made popular by the Clancy Bros. in the 1960s. The [Silber] entry is that song. - PJS - RBW
Logsdon observes that T. S. Eliot included a verse of this in _The Cocktail Party_.- RBW