I have combination, v sensitive skin, and use oil a lot - the key is to find an oil that suits your skin, a lot of creams use sunflower oil as a base (it's very stable) but I personally don't like it; Jojoba and Sweet Almond are much better if you have combination to oily skin.
Try and get samples and try a few, and see if you can work out what you like, then look for products containing those base oils. Don't go by the "oily/comb/dry skin" labels, just try the product on the inside of your wrist, or, ideally, your neck.
I use creams that are supposedly for oily, combination and dry, (I have lots) and vary them depending on whether I'm wearing make up, the time of the month, the weather, etc
There is a v cheap natural brand called Skin Blossom, they stock it in John Lewis and Whole Foods, their products are about £10. The other cheap one is Organic Surge, used to be stocked in Boots, but no longer, you can order online.
What you can always do is try to find a light day cream, then just buy some plain jojoba oil (from Fushi online or in Holland Barrett) and use that at night.