Irony of Zuleika
Zuleika is a beautiful, charming girl who wants nothing more than to find romantic satisfaction with someone who truly loves her. Her only qualification for such a soulmate, however, appears to be that he ... doesn't love her? Anyone who exhibits affection for her based on her appearance is automatically discounted from Zuleika's considerations, and, since all men are attracted to her, it appears she will be single forever. She loves the Duke precisely because he shows no attraction for her, but when she finds out that he did, in fact, love her, her love for him is revoked and her dreams shattered.
Irony of the Duke of Dorset
The Duke of Dorset is a serious, talented young man who seems to have a sense of duty and responsibility for himself and his family. He, having a solid head upon his shoulders and a firm grasp of sober reality, appears to be the least likely person at Oxford to fall for Zuleika, yet he does so anyway. His ironic character twist is so dramatic, furthermore, that he resolves to kill himself as a result of Zuleika's rejection, and he eventually commits suicide as a result of some sort of bad omen. His character is therefore supremely ironic; despite appearing to be the sanest person in the novel, he is in fact the one with the least grounding in reality.
Irony of Noaks
Noaks is a small, unattractive, simple young man, and nearly everyone dislikes him. Despite his untowardness, however, he falls in love with Zuleika as well, and, although being the sole abstainer from the mass suicide of the Oxford undergraduates, he later kills himself as well, demonstrating that even he isn't impervious to Zuleika's charms, and he is just as insane as every other undergraduate in the university.
Irony of the Oxford Staff
When the entire undergraduate population of Oxford University commits suicide, the university staff don't really notice the fact that they're gone, just continuing on as they were. This dramatic irony is a hilarious stab at Oxford, as well as the tendency of men to become obsessed with women, making this catastrophic series of events nothing out of the ordinary.
Irony of the Piano Concert
The Duke of Dorset, being a rather talented young pianist, gives a piano concert to the undergraduates of Oxford. Even Frederic Chopin himself shows up, moved to tears by the Duke's performance. Despite this beautiful music, the concert is ironically the moment that solidifies the desire in the hearts of the Oxford students to commit suicide for Zuleika along with the Duke, as they see Zuleika praise him for the concert and subsequently feel the general attitude amongst the crowd that dying for her would be the noblest of ends.