Cathleen ni Houlihan's identity (Dramatic Irony)
Anyone who was attending this play in its first performances would have likely been familiar with the mythic character of Cathleen ni Houlihan and what she represents. Thus, this would presumably create a dramatic irony in which the audience knows the Old Woman's supernatural identity before the family does. This dramatic irony only functions if the audience knows the story of Cathleen ni Houlihan already.
Michael forgets his wedding (Situational Irony)
By the time that Cathleen ni Houlihan is about to leave, Michael has completely forgotten his wedding and the woman he plans on marrying. While the beginning of the play is all about the family's preparation for the wedding and Michael's devotion to his wife-to-be, all of this completely falls away after the Old Woman's visit, an ironic turn of events.
Cathleen becomes a young woman (Situational Irony)
There is also an ironic twist at the very end of the play, when the family asks Patrick if he saw Cathleen ni Houlihan when he was coming down the path. He describes a young woman, walking like a queen, which reveals to us that Cathleen ni Houlihan has transformed herself, an unexpected moment of magic.
