I was doing some research into onryo, and wikipedia mentions in paragraph form a mythic story of an onryo who terrorizes a village until she was banished.
Although I don't have a lot of specific info on how to banish an onryo (which is what I need to know for writing purposes!), I have a few working theories. One possible way to fight an onryo is to become one yourself. Wouldn't recommend it, since it's kind-of a permanent thing.
Another possibility which crosses my mind is to give the onryo what he or she wants. Onryo seek vengeance or closure, which they never seem to find because it's misdirected. Completing the unfinished business, is a good working theory.
I wish I knew of some good myths and legends that specifically tackle defeating and banishing an onryo, and I'm hoping someone here might have heard of any. The only other thing I can say I've learned from my google search on the subject, is that however an onryo IS defeated (appeased, sated), the winner of the battle must honor the spirit of his foe to complete the banishing and keep the onryo from returning.