Change your cleanser to a cleanser for normal or dry skin. Only use products for oily skin on the areas that breakout often. Your best bet is to ensure your cleanser is "milkly" I've found that most gel cleansers are too harsh, giving you the results that Marina mentioned above.
My recent favorite over the counter find is Dove Energy Glow skin brightening facial cleanser, (and gentle exfolliant). It lists itself as being for maturing skin but "I like it!". It comes in a yellow-tube.
I use Aloe Vera Barbadensis Jelly which is great for oily skin. It helps soothe skin problem areas and penetrates quickly for faster and deeper soothing power. Excellent as a light weight moisturizer for excessively oily skin and extremely effective for blemished skin.
Oily Skin:The selection of cleansers for oily skin should involve using products that rinse off well, both bar soaps and liquid cleansers have been formulated for this purpose. Many of the soap gels and stronger liquid cleansers are helpful for oily skin. Because the skin on the face, chest, and back is oilier than the rest of the body, it may be necessary to use one product on these areas, and a more moisturizing product on the arms, legs, hands, and feet. Many of the cleansers which are appropriate for acne-prone skin, would be suitable for oily skin.