Certainly Wharton shows her expertise in the area of irony in her writing, and this great novel is no exception. Centrally, irony is used to indicate the hypocrisy that is at the heart of the society of New York. For example, you might like to consider the snobbish attitude that is revealed by the Welland family when they go to St. Augustine for the winter with a group of servants to help them survive the deprivation of being away from town. At one point, as they sit down to an incredible breakfast, Mr. Welland comments to Newland:
You see, my dear fellow, we camp—we literally camp. I tell my wife and May that I want to teach them how to rough it.
Clearly, there is no "roughing it" in such luxurious surroundings and with such people, and Wharton makes us laugh at the presumption of such characters as she exposes their various foibles.
Of course, whilst a considerable amount of the humour in this novel is thanks to irony, at the same time, irony also lends itself to augment the central tragedy of this novel. Let us remember that Newland's association with Ellen begins when he is sent to talk her out of divorcing her husband, thereby sacrificing personal happiness for the happiness of her family. When he falls in love with Ellen, she has learnt his lesson so well that she refuses to run away with him because it would hurt May. Personal happiness is something that, with bitter irony, must come second place to the happiness of the family and others.
Therefore, in answer to your question, I would want to explore the way in which irony is both used to criticise, sometimes incredibly humorously, but also it is used to create the real sense of tragedy that dominates this novel.