He was educated at Rockwell College and Garbally, Ballinasloe, becoming for a time a Jesuit scholastic.
In his autobiographical book, The Singing Masters, O'Meara describes the hard times of his childhood, including the terror brought by the British Black and Tans, and by the subsequent Irish Civil War.
The Singing Masters also describes war-time Oxford and the antiquated (and quaint) conditions in which he studied there.
O'Meara held visiting appointments at the Princeton Institute of Advanced Study, Dumbarton Oaks (Harvard University) and Vassar College.
In Ireland he played a major role in the effort to modernize education in the schools and universities, in particular the teaching of Latin and Irish, and the collaboration between University College Dublin and Trinity College Dublin.