An epigram is a pithy saying, usually humorous. Mark Twain was responsible for many striking, mostly cynical epigrams, such as “Always do right. That will gratify some of the people, and astonish the rest.” (Unfortunately, he was also responsible for an even more famous one that has been confusing people ever since: “Everyone is a moon, and has a dark side which he never shows to anybody.” It’s true that the moon keeps one side away from the earth, but—if you don’t count the faint glow reflected from the earth—it is not any darker than the side that faces us. In fact, over time, the side facing us is darkened slightly more often because it is occasionally eclipsed by the shadow of the earth.)
An epigraph is a brief quotation used to introduce a piece of writing or the inscription on a statue or building.
An epitaph is the inscription on a tombstone or some other tribute to a dead person.
In literature, an epithet is a term that replaces or is added to the name of a person, like “clear-eyed Athena,” in which “clear-eyed” is the epithet. You are more likely to encounter the term in its negative sense, as a term of insult or abuse: “The shoplifter hurled epithets at the guard who had arrested her.”