Born in Cork, O'Dwyer trained as a barrister, while writing articles for periodicals.
He won the seat, and was re-elected at the 1835 UK general election, but was then unseated on petition.
He stood in the resulting 1835 Drogheda by-election and was re-elected, but as he had already been deemed ineligible, his opponent, Randall Edward Plunkett, was instead awarded the seat.
[1] In 1837, O'Dwyer was appointed as the filacer of the exchequer, serving until the office was abolished in 1845, and then received a substantial pension.
[2] At the 1857 UK general election, he stood in Waterford City as a Radical, but took last place.