Maybe wash with Neutrogena Oil Free Acne Wash Facial Cleanser, Pink Grapefruit which has 2% salicylic acid? Also Neutrogena makes a great beta hydroxy acid (BHA) - Oil Free Acne stress Control, 3 in 1 Hydrating Acne Treatment. You would use that at night after cleaning your face. BHA helps clean the pores out. It is an exfoliator.
It is important to use sunscreen every day also. The BHA I mentioned will make you more sun sensitive. I know that with oily skin finding a sunscreen you can use can be really frustrating. Many sunscreens just make you oilier and make your face break out all the more. I have been having success with Blue Lizard for Faces spf 30.
And, lastly, it sometimes helps to use a primer over the sunscreen. Particularly if you want to use makeup. I have found that Monistat Anti-Chafing Powder-Gel actually works really well as a primer.
Now all that being said I used to have a lot more oil and a lot more problems with breakouts myself. What slowed down the oil production on my face and stopped my cystic acne breakouts along the jawline was switching to oil cleansing. (Just google oil cleansing method and you can read about it.) It worked for my skin. It may or may not work for you. My skin is still oily and sensitive but not as oily and I don't get breakouts anymore.
That is true Ally but the product mentioned is one that comes highly recommended and it would not ADD to the problem. If you would rather go the milder route you could always use Dove bar to wash your face with. It is mild and not irritating. It won't cause your face to produce even more oil.