Cyst are painful "red" looking bumps. They are harder to get rid of because the problem lies deep within your skin. I used to have many cyst, accutane made them go away. What I came to find out was the cyst were caused by me irritating my pimples by popping them. When I popped the pimple, some of the sebum was pushed further into the pore, causing it to later become infected and causing cysts.
Oil is not the cause of acne. You sort of answered your own question. "if oil is the cause of acne then how do some people have really oilly skin and no acne and some people have dry skin and bad acne?"
There are MANY factors of what causes acne. Each indivdual has their own causes for acne. Some it's hormonal, some it's uncleaniness, some say it's the food they eat, etc. etc. Find out what could contribute to your acne.
Sebum, which is the excess stuff your body doesn't digest is pushed through the surface of your skin, sometimes it gets trapped, it gets infected, and then boom, you have a pimple.
Dry skin can also be a contributing factor to acne, sebum/oils have to move through your pores, it's somewhat like a car, you have to put "oil" into it to make it run smooth, make sure all the gears are lubbed. Like your skin, you have to moisterize, it also decreases the amounts of dry dead skin flakes which could potenially block pores. So...use facial lotion, even if you're a guy.