The song seems to come from The Agreeable Surprise, a one-act comic opera written in 1781 by John O'Keefe, with music by Dr Samuel Arnold. The play was an adaptation of a piece by Marivaux, L'Heureux stratagème. Offhand I don't know where you'd find the music.

Heavy classical allusions of the kind seen in this song were very much used in the 18th century, and continued to be popular in Ireland long after they had dropped out of favour elsewhere. Any Classical Dictionary will provide details. Decent public libraries have them, and some are available online: there is one at http://www.beazley.ox.ac.uk/CGPrograms/Dict/ASP/OpenDictionary.asp, for example. Bear in mind that you may have to try alternative spellings for some words.