He played for Boston College from 1978 to 1982. The Los Angeles Kings chose him 157th overall in the 1980 NHL Entry Draft. O'Dwyer turned pro with the Kings in 1982-83 but spent the bulk of the next three seasons with the New Haven Nighthawks of the American Hockey League. The Kings only called him up for 18 games in that stretch. Signing as a free agent with the New York Rangers made little difference, as O'Dwyer played all of the next two seasons with the Nighthawks. O'Dwyer signed as a free agent with the Kings in 1990. After two seasons of minor pro, he retired in 1992.