Jerome and Theodore (Dramatic Irony)
There is dramatic irony when Jerome decides to pretend that Theodore and Isabella have a romantic understanding. This ends up backfiring because Manfred decides to execute Theodore; it is also rendered more ironic when we discover that Theodore is Jerome's son. Another level of irony is that Jerome's actions will later lead to the death of Matilda because Manfred mistakes her for Isabella and rages against her meeting with Theodore.
Mistaken Identities (Dramatic Irony)
The dramatic irony of the text is quite obvious when it comes to the mistaken identities. Theodore vows to fight the great knight to defend Isabella, but ends up wounding her father instead. Manfred murders his own daughter at the end of the novel because he thinks she is Isabella. The readers could intuit that this was coming due to Manfred's obsessive jealousy of Isabella's (fake) relationship with Theodore; in contrast Matilda, Theodore, and Isabella had no idea that this was going to happen.
Matilda and Theodore (Dramatic Irony)
Another use of dramatic irony is Matilda falling in love with the very person who signals the ruin of her family's claim to Otranto. Theodore will supplant her and her family, but she cannot help her feelings. This sets the events of the story on a crash course towards tragedy.
Family Relations (Situational Irony)
Manfred's claim that he and Hippolita are related, which he proffers as a reason for divorce, is supremely ironic given the fact that he has no qualms pursuing incestuous designs against Isabella and does not even seem to register them as such.