The Necklace's Worth (Dramatic Irony)
The main irony in the story is that the Loisels take on tremendous debt in order to replace an apparently expensive necklace that was actually a cheap imitation.
The Rise and Fall of Mme. Loisel (Situational Irony)
Mme. Loisel is dissatisfied with her place in society at the beginning of "The Necklace." In her efforts to pretend to be higher class by borrowing a beautiful necklace, she and her husband end up even lower in society.
Mme. Loisel's Response to the Invitation (Situational Irony)
M. Loisel expects that Mme. Loisel will be excited by an invitation to a fancy party, since his wife often bemoans the lack of elegant things in their life. However, Mme. Loisel becomes even more distressed by the prospect of the party because she feels she does not own the clothing and jewelry necessary to attend properly.