damaged but oily hair

Cut off the damaged parts. You can't do anything about them and they will make everything else look bad.

As for the rest of it - here's what I do - I wash my hair normally and then I only condition from about a half an inch above my ears to the tips. For the roots (my scalp), I shampoo a second time. This gets the ends conditioned without making my scalp oily. I just use regular shampoo but if your scalp is really oily, you might want a third product so, instead shampooing a second time with the first shampoo, use one for oily hair just for the roots. It might be more complicated and take longer, but it should work.

Note: I am not a hairdresser; this is just what has worked for me.