While plenty of Irish actors and actresses have staked their claim in Hollywood, perhaps there aren't as many as one would assume. For example, IMDB recently released their list of the most 'popular' Irish actresses in the world, and Saoirse Ronan is leading the list.
Keep in mind, IMDB would use their own metrics to come up with this honor, probably based on the number of IMDB page views. Of course, Saoirse has established herself as major A-lister over the past few years, gaining an Oscar nomination for Atonement and then cementing her 'upcoming star' status with Hanna, The Host, and The Grand Budapest Hotel.
She was supposedly rumored in contention for the Scarlett Witch role in The Avengers, and it was even rumored that she was also being used to create the character's likeness in pre-production, but the role eventually went to Elizabeth Olsen instead. And then, there were also rumors about Saoirse joining the Star Wars franchise, especially after she confirmed that she had met with the film's director, JJ Abrams. However, the creators ended up going with mostly untested film stars, and as this IMDB list proves, Saoirse is too well-known to actually be considered untested anymore.
Second place on the list is Michelle Fairley, best known as the Catelyn Stark on Game of Thrones. Eve Hewson came in third place, which was no doubt due to her status as Bono's daughter rather than any of her individual career achievements at that point.
Of course, there are a lot more Irish actors in Hollywood than actresses, purely as a result of the mis-matched gender politics in the industry. People like Cillian Murphy, Colin Farrell, Jonathan Rhys Meyers, Ciaran Hinds, and of course, Michael Fassbender, have all made it as Irish actors in Hollywood, but their female counterparts are few and far between.