A friend of mine has really pretty, healthy-looking hair, and my dried out mop needs some love and attention (not to mention my scalp), so I asked her about her hair regimen. Like me, she just uses a simple, non-harsh shampoo (Head & Shoulders Classic Clean for me, Tesco Value store brand for her).
The bit where it gets interesting is her "pre-conditioner": she massages sunflower oil into her scalp and hair and then rinses it off before shampooing (3 times a week). So I thought, "hey, why not?" It certainly seems to work for her, and I've got some in the pantry, so I'll give it a try!
...But then I remembered that my face has oily skin issues and I should perhaps proceed with caution. I tried searching this board for the word "sunflower", but got nothing. ...Perhaps I should stop being such a wuss and just try it already? I just figured I'd ask if anybody else had any experience with it.
Oil in your hair might be a good idea, though I'd only use a few drops. However, there may be more beneficial kinds of oils out there (such as emu oil), you might want to search online and decide what you might like to try.
I'd say the worst that could happen is a breakout, then you would simply stop using the oil - but you won't know unless you try.
Also, pure African "Black Soap" is supposedly extremely beneficial to your hair, and you may consider that as well. While many have had the greatest hair they've ever experienced (and facial skin as well) by not washing at all; sounds dirty, and is a big step to take, but in time your scalp and skin will thank you.
If you want to consider perhaps ending your oily facial concerns, you can send me a message and I'll try to help : )