Some protection. Extra virgin oil doesn't have any proven healing properties above other oils. That said, you can relieve dryness and some superficial irritation temporarily with oil on your skin. Lena horne, who was one of the classic beauties of our time once said that she never washed her face and only applied olive oil to her lovely complexion every night. I think she was just blessed with great genes.
Dry skin. Olive oil has been used for cradle cap and dry skin due to its emollient properties. If you don't like the smell, almond oil is another great option.