An asteroid is a rocky, sometimes metallic, body that is smaller than a planetoid/minor planet.
A comet is body composed largely of ice and aggregate rock. They often orbit the sun in an extremely elliptical orbit. As it approaches the sun, ice vaporizes creating a tail.
A meteroid is a fragment of either an asteroid or a comet.
As for the suffixes:
meteoroid - in space
meteor - the streak of light of a meteoroid traveling through the atmosphere
meteorite - on the surface