If you think face oils are for dry or dehydrated skins only then you must read this. 

If you have oily skin, nourishing non-congesting facial oils can help mimic the natural skin sebum(oil) which in turn sends signals to our oil producing glands to stop producing more oils.
On the contrary, if you are using the products created to "dry out" the oily skin, it will actually trigger the oil glands to increase oil production, which only worsen the oily skin problem.

And if you have dry skin then facial oils locks in the moisture keeping it hydrated all day long.

Facial oils can also help calm the skin irritation, itchiness and inflammation.