Dramatic Irony is the expression of one's meaning by using language that normally signifies the opposite. In Julius Caesar there is Dramatic Irony when Caesar is warned about the Ides of March by the soothsayer.
Foil is a character who contrasts with another character, usually the protagonist. Foil is used in Julius Caesar when they both conspire to kill Caesar, Cassius is more likely to lean on treachery and tricks and to play on ambition than Brutus is.
Verbal Irony is which a person says or writes one thing and means another. Verbal Irony is used when Cassius is speaking to Brutus in Act I. Cassius tries to convince Brutus that Caesar is not worthy to be the leader of Rome.
Situational Irony is when incongruity appears between expectations of something to happen, and what actually happens instead. Situational Irony is used in Act 3, when Caesar proclaims that he is "constant like the North Star" shortly before he is killed by the Senators.
Catastrophe is an event causing great and often sudden damage or suffering. It is used when Brutus tells his servents to hold out a sword to he can can run into it.
Soliloquy is an act of speaking one's thoughts aloud when by oneself or regardless of any hearers, especially by a character in a play. Antony delivers a soliloquy when he addresses Julius Caesar's dead body by himself.