The word you use, "hard&oil," is kind of difficult to understand, but I use natural coconut oil (it turns to a soft solid if kept in the fridge, so it is like a cream). I get it in the health-food section. It's great for the skin.
There are various types of natural skin cleansing products in the market. You can use those to avoid further skin irritation. Chemically-derived products often have drawbacks after some time of using it.
Garnier Skin Naturals Oil Control Fairness Cream is one of the good cream for those who have oily skin.