Indebted (Situational Irony)
Even though the Old Man is the one who bankrupted the Student's father, he is able to weasel his way into the young man's trust. In a matter of moments, he convinces the Student that it was his father who wronged him, not the other way around. In an ironic twist of fate, the debtor is able to convince the son of the indebted that he is the one owed something.
The Milkmaid (Dramatic Irony)
While the audience (and the Student) can see the Milkmaid—a ghost, presumably—the Old Man cannot, which creates an instance of dramatic irony, in which we see something a character does not. While we do not initially know the full significance of the Milkmaid, we know that she is a threatening figure to the Old Man.
Old Man in the hall (Dramatic Irony)
As Johansson and Bengtsson gossip about the Old Man, he appears in the hallway, unseen by them, and listens in. This is an instance of dramatic irony, in which the audience can see something that the characters cannot.
The Mummy kills the Old Man (Situational Irony)
The Old Man goes into the Colonel's home with the intention of killing the Colonel and his guests in an act of vengeance. Ironically enough, however, he is the one who ends up perishing, when the Mummy takes matters into her own hands and reveals him to be an evil and duplicitous man.