An asteroid is a rocky object in space that's not as big as a planet and isn't a moon. There are millions of them, think the asteroid belt in space. A meteor is an asteroid that burns up as it enters the Earth's atmosphere, think shooting stars. A meteorite is a meteor that actually lands on the surface of Earth, think about Russia today.
As for a meteoroid? No one really knows. They're just kind of like smaller asteroids. More here.