When your skin is oily, the assumption is that to stop the oil and breakouts, you need to dry out your skin, and avoid things like moisturizer.
But when you irritate oily skin by drying it out, you're making things worse. When the oil-producing glands get dry, they think they need to help you get back to normal by producing even more oil. (READ: When you dry out your skin, it actually makes it more oily.)
Go with oil-free products, and you'll be able to cleanse without over drying.