Verbal irony is expressed by Mathilde when her husband brings home the invitation and she says "I have no gown, and, therefore, I can't go to this ball. Give your card to some colleague whose wife is better equipped than I am." Mathilde doesn't really want her husband to give the invitation away, she is being sarcastic which is the most common form of verbal irony. She wants a new dress.
Situational irony is expressed most clearly in the ending of the book when Mathilde learns that the necklace she has gone into poverty to replace was actually a fake. Situational irony is when an outcome is the opposite of the expected outcome.
Dramatic irony is expressed through Mathilde's rejection from a part of society she so desires to be a part of. Dramatic irony is when the audience knows something that the characters do not and we can see her rejection more clearly than she. We can also see that her life really isn't that bad, which she has trouble recognizing because she is so worried about the things others have.
Situational irony results when there is a weird coincidence or unfortunate set of circumstances in a given situation. Situational irony in this story occurs because Madame Loisel really wants to be in the upper class, but because she insists on borrowing the necklace, she ends up in an even lower class than when she started.
Verbal irony occurs when the speaker what is said is opposite of what is meant. A common type of verbal irony is sarcasm. In this story, when Madame Loisel sits to dinner with her husband and says, "Ah, the good soup! I don't know anything better than that," she really means that she is unsatisfied with her dinner.
Dramatic irony is a result of the characters not being aware of their situation. In these cases, the audience is typically more aware than the characters in the story itself. However, the moment of realization at the end of the story, when Madame Loisel and the audience discover at the same time that the necklace is fake is an example of dramatic irony. The assumption that it was real is what makes it this type of irony.