Asteroids, orbit mostly between Mars and Jupiter in the Asteroid belt. They have regular orbits generally, the largest ones are often called planetoids, Ceres for example which I belive is about 60miles long.
Comet's have irregular orbits, are generally made of dust and Ice, orgintate from the Oort cloud, eg Haleys comment takes about 72 years to orbit the sun. They usually have a very eccentric orbit passing close to the sun at one end of the elipse and disappearing for, in some cases, thousands of years before being sreen again.
Meteors are usually what you would call shooting stars that burn up into the atmosphere. They are usually very small. They are debris that is encountered by Earth as we orbit. If one hits the groud it is known as a meteorite. Stand by for a load of pendantic rambling about the tunguska incident.
As always there are exceptions, I have described the general situation.