Synonyms for Avenge:

n.

defeat, thrash, knock out, smash, beat, overcome, win, crush, overpower. requite, settle an (old) score (with someone), get your own back, respond in kind, hit back, get back at, fix, pay back, wreak, forgiveness, even the score, get even with, pay off, take an eye for an eye, get/be even (with someone). avenge (noun)
retaliate, revenge.

v.

competition (verb)
retaliate, revenge.
punish (verb)
correct, try, pillory, incarcerate, execute, afflict, punish, persecute, crucify, lambaste, torture, anguish, fine, imprison, judge, castigate, Keelhaul, discipline, burden, chasten, agonize, distress, chastise, penalize, sentence, confine, reprise.
retaliate (verb)
punish, return fire, get back at, retaliate, respond, Retribute, chastise, counteract, even the score, repay, revenge, redress, retort, vindicate, counterblow, exchange, chasten, countercharge, reciprocate, requite, counter.
revenge (verb)
restitute.

Other synonyms:

get even with, get back at, hit back. pay back, wreak. fix. revenge
hit back, take an eye for an eye.
Other relevant words:
get even with, even the score, beat, fix, pay back, get back at, take an eye for an eye, pay off, requite, wreak.

Usage examples for avenge

  1. Shall we not avenge him? – The Chouans by Honore de Balzac
  2. I do not want to avenge myself. – Andreas Hofer by Lousia Muhlbach