These terms have, on the surface, the similarity that they are “non-tragic.” Aristotle, whose Poetics treatise “On Tragedy” influenced so much of western literature, wrote another treatise called “On Comedy,” but it did not survive. Let us look at the individual terms usually connected with comedy:
“Humour” (or “humor”) is a general term signifying a non-serious reaction to the literature by the audience, a light-hearted, frivolous, whimsical reaction, caused by an unexpected departure from reason or sense—a play on words, a clever analogy, an understatement, etc.—(“Who was that lady I saw you with? That was no lady, that was my wife.”) It can have a hidden threat or criticism in it (Canetti says “Laughing is baring your teeth at the enemy.”) but is not to be taken seriously. Its function is to momentarily amuse the reader or audience member.
The best summary of comedy is “tragedy avoided.” That is, the development of plot and character does not fulfill the requirements of tragedy: A great figure fallen from a high place, catharsis, etc. Usually the dramatic tension in comedy comes from the audience’s fear that a catastrophe will not be avoided.
“Irony” is not really comic. The formal definition is “What goes out as A comes back as non-A.” That is, the intention of a statement is superseded by its actual effect. I will survive this ordeal or die trying” is an ironic statement. However, irony is usually imbedded in a circumstance, where the observer make a conclusion different from the participant’s intention.
“Satire” is a more formal comic type, one in which behavior is exaggerated to criticize or to condemn. The television show Saturday Night Live is full of examples, where current events, people in the news, celebrities, etc. are depicted with exaggerated condensation of recognizable traits and habits, for comic effect.
It should be noted that all these term can be used in other art forms than just literature.