Now, I think I know the answer to my own question, since exorcism is a ceremonial blessing, and Byzantine tradition limits ceremonial blessings to priests only. But, since the question of "who can exorcise" has gone through various levels of laxity and strictness in the history of the Roman Church (with the 1983 Code of Canon Law being perhaps the strictest situation), I was wondering what the rules generally were in the Eastern Churches?
(e.g., only priest designed by the bishop, any priest, priest or deacon, etc.)