He worked in insurance until taking up acting. Other films in which he appeared include: , The Fallen Idol (1948, again for Reed, and again as a police inspector), Alfred Hitchcock's , The Bad Lord Byron (1949), Landfall (1949), Disney's Treasure Island (1950), Marry Me! (1950), Captain Horatio Hornblower (1951), The Long Dark Hall (1951), Mogambo (1953. Another John Ford film), Niagara (1953), Never Take No For An Answer (1953), The Rising of the Moon (1957), Captain Lightfoot (1957), Darby O'Gill and the Little People (1959) and Esther and the King (1960).
O'Dea was a leading member of Dublin's Abbey Theatre, where his work led to a number of notable film roles, including two mid-1930s John Ford films, The Informer (1935 film) and The Plough and the Stars (1936), and the part of the police inspector in pursuit of IRA man James Mason in Carol Reed's Odd Man Out (1947).