Chemical reactions where two species come together usually require some sort of collision (these are called addition reactions). In general adjusting any condition that increases the likelihood of a collision is going to increase your rate.
As you stated, if you increase the temperature, the oxygen atoms will move faster and the likelihood of collision increases.
If you increases the pressure by decreasing the volume, it means that the oxygen atoms will be more likely to come in contact with the solid carbon, as it is confined to a smaller space.
If you increase the amount of oxygen, then there is more of it, so more likely for a collision.
Likewise, if you increase the amount of carbon, there is more carbon to collide with, so it should increase the rate.
For these types of reactions, it is helpful to view the reaction as a collision, which coincidentally enough, is where the basics behind "Collision Theory" come from:
http://en.wikipedia.org/wiki/Collision_theory