I'm going to assume that you meant "my skin" not "mouth skin". If you meant mouth skin, i'm going to assume that using a mouthwash would assist in keeping it "fresh" and the alcohol within the mouthwash would help with any bacteria etc.
As far as keeping your skin healthy and un-oily...
-Limit your fatty foods intake. "You are what you eat"... by consuming foods that are high in oil, you are more likely to have oily and unhealthy skin as a result.
-Wash in the mornings and at night. Be sure to use a moisturizer that is low in oils, you don't want to add anymore to the skin.
- Use oil cloths, such as neutrogena. They are to blot the skin during various hours of the day when washing your face is not an option.
-If you have longer hair... the natural oils from your hair may be heavy- leaving residue on your skin. You can use a clarifying shampoo 1-2x weekly to strip your hair of its natural oil and buildups.