Irish sweep the boards at prestigious Laurence Olivier Awards
O'Hanlon has been nominated in the Best Supporting Actor category for his role in Conor McPherson's 1997 play 'The Weir' and will go up against 'Sherlock' star Mark Gatiss and 'Mr Selfridge' actor Ron Cook.
The Cork native said she was "shocked" and "thrilled" when she heard the news.
“I'm speechless. It's a massive honour - one which I wasn't expecting," she told the Irish Independent.
The Olivier Awards ceremony will take place at the Royal Opera House on April 13, and broadcast later that evening on ITV.
Unfortunately, none of the cast of McDonagh's production will be able to attend the ceremony as they will be treading the boards on Broadway.
Following on from its West End success, the dark comedy has been transferred to New York's Cort Theatre and will begin its run on April 12.
"Being on stage on Broadway is a good excuse for not going," Greene said. "Plus I'd be such a nervous wreck it's probably a blessing in disguise."
Playwright Conor McPherson's production of 'The Night Alive' has been nominated in the 'American Airlines Best New Play' category.
The play, which stars 'Love/ Hate' actress Caoilfhionn Dunne, Brian Gleeson, Ciarán Hinds and Jim Norton will go up against Lucy Kirkwood's 'Chimerica' and John Logan's 'Peter and Alice'.
Musical 'Once' based on John Carney's 2006 film starring Glen Hansard has got the nod in the Mastercard Best New Musical category and will go head to head with controversial show 'The Book of Mormon', childhood classic 'Charlie and the Chocolate Factory' and 'The Scottsboro Boys'.
Eight time Tony Award winning musical 'Once' has picked up several nomination including Best Choreography, Best Sound Design and Best Set.
Glen Hansard and actress Markéta Irglová Autograph have also been nominated in the Autograph Sound Award for Outstanding Achievement in Music.
While the Almeida Theatre's production of 'Ghosts' starring Monaghan actress Charlene McKenna has received a nomination for Best Revival.