O’Shea is raised in Dublin and educated by the Christian Brothers at Synge Street CBS, along with his friend Donal Donnelly. His father is a singer and his mother a ballet teacher. Because he is bilingual, he performs in English-speaking theatres and in Irish in the Abbey Theatre Company. At age 12, he appears in George Bernard Shaw‘s Caesar and Cleopatra at the Gate Theatre. He later studies music and drama at the Guildhall School of Music and Drama in London and is a skilled pianist.
O’Shea is discovered in the 1950s by Harry Dillon, who runs the 37 Theatre Club on the top floor of his shop, the Swiss Gem Company, 51 Lower O’Connell Street, Dublin. Early in his career he tours with the theatrical company of Anew McMaster.
O’Shea begins acting on the stage, then moves into film in the 1960s. He becomes popular in the United Kingdom, as a result of starring in the BBC sitcom Me Mammy alongside Yootha Joyce. In 1967–68 he appears in the drama Staircase, co-starring Eli Wallach and directed by Barry Morse, which stands as Broadway‘s first depiction of homosexual men in a serious light. For his role in that drama, he is nominated for the Tony Award for Best Actor in a Play in 1968.
O’Shea stars as Leopold Bloom in Joseph Strick‘s 1967 film version of Ulysses. Among his other memorable film roles in the 1960s are the well-intentioned Friar Laurence in Franco Zeffirelli‘s Romeo and Juliet (1968) and the villainous Dr. Durand Durand in Roger Vadim‘s counterculture classic Barbarella (1968). In 1984, he reprises his role as Dr. Durand Durand, credited as Dr. Duran Duran, for the 1985 Duran Duran concert film Arena (An Absurd Notion), since his character inspired the band’s name. He plays Inspector Boot in the 1973 Vincent Price horror/comedy film Theatre of Blood.
O’Shea is active in American films and television, such as his memorable supporting role as the trial judge in the Sidney Lumet-directed movie The Verdict (1982) with Paul Newman, an episode of The Golden Girls in 1987, and portraying Chief Justice of the United States Roy Ashland in the television series The West Wing. In 1992, he guest stars in the season 10 finale of the sitcom Cheers, and, in 1995, in an episode of the show’s spin-off Frasier. He appears in the pilot episode of Early Edition as Sherman.
Other stage appearances include Mass Appeal (1981) in which he originates the role of Father Tim Farley, for which he is nominated for the Tony Award for Best Actor in a Play in 1982, the musical Dear World in which he plays the Sewer Man opposite Angela Lansbury as Countess Aurelia, Corpse! (1986) and a 1994 Broadway revival of Philadelphia, Here I Come!.
O’Shea receives an honorary degree from Quinnipiac University in 2010.
O’Shea’s first wife is Maureen Toal, an Irish actress, with whom he has two sons, Colm and Steven. They divorce in 1974. His second wife is Irish actress Kitty Sullivan, whom he meets in Italy, where he is filming Barbarella and she is auditioning for Man of La Mancha. The couple occasionally act together, such as in a 1981 Broadway revival of My Fair Lady. O’Shea and Sullivan have no children together. They both adopt United States citizenship and reside in New York City, where they both live from 1976.
O’Shea dies on April 2, 2013, in New York City following a short illness at the age of 86. He is buried at Deans Grange Cemetery.