Off can be many parts of speech, depending on the meaning. Most often an adverb or preposition, but also an adjective, noun, or verb.
adverb
- Away from the place in question; to or at a distance.
- So as to be removed or separated.
preposition- Moving away and often down from.
- Situated or leading in a direction away from (a main route or intersection).
adjective- Characterized by someone performing or feeling worse than usual; unsatisfactory or inadequate.
- (of food) No longer fresh.
noun (cricket)- The half of the field (as divided lengthways through the pitch) toward which the batsman's feet are pointed when standing to receive the ball.
verb(informal)- (North American) kill; murder.