Roland (Dramatic Irony)
Throughout the play, the British soldiers for whom Owen work call him "Roland," which is a mistake. While the audience knows his name is Owen, the soldiers get it wrong every time, which shows their disrespect for him.
Owen's translations (Dramatic Irony)
When Yolland and Lancey visit the hedge-school, Owen translates their statements for them, but takes many liberties in his translation. We the audience can hear that he is changing the wording of Lancey's speech, but Lancey, who does not speak Gaelic, has no idea, which creates some comic dramatic irony.
Owen and Yolland defend each other's positions (Situational Irony)
One of the central ironies of the play is the fact that Owen, a native of the village who seems like he ought to be more invested in the preservation of its traditions, is the most eager to "standardize" the language for English-speakers. On the flip side, the Englishman Yolland is invested in the Irish language, and sees the project of the Red Coats as "an eviction of sorts." Both of these men are, in a way, "disloyal" to their respective countries, with Owen taking a more English point of view, the perspective of the colonizer, and Yolland empathizing with the Irish, the colonized.
Maire and Yolland (Dramatic Irony)
Maire and Yolland strike up a mutual affection, and in Act 2, Scene 1, they find themselves alone after the dance, trying desperately to communicate even though they do not speak the same language. Even though, to the audience's ears, they both speak English, Maire is in fact speaking Gaelic. Thus, the audience hears the meaning of what each of them is trying to say, but they themselves have no idea what the other is saying, which creates a rather comic and romantic instance of dramatic irony.