O'Heaney has worked extensively in live theater, but is best known for playing Sarah Stickney White, the female lead on the ABC series Tales of the Gold Monkey in the early 1980s.

She moved to Broadway to understudy the role of Elizabeth in A Matter of Gravity, starring Katharine Hepburn and co-starring her Juilliard friend and colleague Christopher Reeve.

She relocated to Seattle to appear as Celia in As You Like It, Gwendolyn in Travesties, and Eylie in Ladyhouse Blues at ACT/Seattle, then returned to New York to play the double roles of Belle and Mrs. Cratchit in A Christmas Carol at Playwrights Horizon.

When A Christmas Carol closed, O'Heaney moved to Los Angeles, and five weeks later she was cast as Anna Marie Hollyhock in the 1978 ABC comedy series Apple Pie, which was produced by Norman Lear, directed by Peter Bonerz, and starred Rue McClanahan, Dabney Coleman, Jack Gilford, Derrel Maury, Mike Binder and Richard Libertini.

"[citation needed] O'Heaney remained in Los Angeles to play fourteen-year-old Bianca in White Marriage at the Odyssey Theatre and won a Drama-Logue Award for Best Actress for the role.

She then returned to the East Coast to star as Ersilla Drei in Pirandello's Naked at the Syracuse Stage, and performances in Ape Watch at the Mark Taper Forum Lab and in The Brides at the Lenox Art Centre soon followed.

In 1982, she was cast in the lead female role of Sarah Stickney White in ABC's Tales of the Gold Monkey, also starring Stephen Collins, Roddy McDowall and Jeff MacKay.