Gossiping about Edward (Dramatic Irony)
In the first scene, Edward goes out of the room for a moment and the guests gossip about the fact that Lavinia is not there and Edward does not know how to throw a party. This is a moment of dramatic irony in which the audience is privy to something that Edward does not see.
Edward's wife has left him (Dramatic Irony)
Edward tells the group that his wife, Lavinia, is away visiting an ill aunt in the country, an excuse which they all accept, if reluctantly. Later, however, while talking to the Unidentified Guest, he reveals that his wife actually has left him for good, and he does not know what to do. This is an instance of dramatic irony, in which the audience knows something that (allegedly) the other characters do not.
Celia and Edward's Affair (Dramatic Irony)
Another scene and piece of information to which the audience is privy, but the other characters are not, is the scene between Edward and Celia in which they declare their love for one another. We learn here that there is perhaps a more specific reason why Lavinia has left Edward.
Lavinia's Affair (Situational Irony)
While it would appear that Edward is the spouse in the relationship who is committing an infidelity, it is later revealed that Lavinia is also having an affair—and with none other than the young man who is in love with Celia, the young woman with whom Edward is having an affair. This is an ironic twist that shows the ways that, not only are the two of them both unhappy, but they have more in common than they suspected.