vindictive
Meaning: vengeful
Usage: The vindictive madman seeks to exact vengeance for any insult that he perceives is directed at him, no matter how small.
wrath
Meaning: vengeful anger, punishment
Usage: Did you really want to incur her wrath when she is known for inflicting the worst punishments legally possible?
avenge
Meaning: to seek revenge
Usage: The team hoped to avenge last year’s loss by winning the rematch.