My hair is so greasy that my pillowcase looks like a paper towel that Ruffles has been sitting on after about three nights. I don't think any frequency of shampooing is damaging my hair at all...
Actually -- hear me out here and, yes, being totally serious about this on a FOOTBALL site -- you may be making it worse. I also have very oily hair. What the sulfates in shampoo do is strip your scalp of its natural oils. What's wrong with that? This signals your sebaceous glands to start making more oil because it's reading your skin as dry. We think, oh, more suds, more better. I have used over the years a baking soda solution (this is really tough on hair), liquid castille soap (Dr. Bronner), but mostly I use a large amount of [cheap] conditioner as my cleansing agent. And then you have to use a technique of getting in there with your hot water and massaging your scalp to loosen the dirt because you don't have all the sudsy damaging lather doing the dirty work. Google "no poo".
ETA: I never understood that "I just washed my hair and I can't do a thing with it" ad campaign YEARS ago or people that, while they take daily showers, don't wash their hair every day. After one day, my hair feels dirty; and if I just took a shower and not washed my hair, I will still FEEL dirty. That's why I can't take night showers in lieu of showering in the morning for the day and expect to feel clean.