Adding to what Mathias said, when you have an uneven, rugged surface (such as clean skin), light will be reflected in varying angles and directions. The visual aspect of the reflection will be fuzzy and distributed, such as we see in velvet, for instance.
On the other hand, on polished or glossy surfaces light bounces on even angles and directions, creating a distinctive area of reflection called specular highlight. The effect is commonly seen on resins, glass, metal and other reflexive materials. If you have oily skin (grease), you eliminate its imperfections, thus creating the clear areas of reflection. It's what you currently have on your piece.
A couple of years ago,
Arne has put together a very concise and yet broad tutorial, that covers most aspects of the basics of the classical approach to painting.
Check out the "Light Stuff" and "Materials" sections for some interesting examples!
Try reducing the specular highlights and you'll reduce shininess (and thus greasiness).
Where exactly is your light source?
