I also have fine & oily hair and no matter how hard I tried to stretch out shampooings, I was always uncomfortable with the greasiness by day 2 (I used corn starch as a dry shampoo, because I'm sensitive to artificial fragrances, but helped the looks but not how I felt). But then about a month ago, I tried 'washing' my hair with water, going through the exact same motions I would if I were shampooing, and I couldn't believe it but it worked! Now I can go 4-5 days between shampooing, as long as I wash with water (very thoroughly, even more thoroughly than with regular shampoo, lol) every shower. I never, ever could have done that before! Obviously, as the days go by my hair feels less silky but it doesn't feel dirty, just more textured/voluminous. So if anyone wishes they could shampoo less but has always had too much build up, that might be something else to try.
ETA: forgot to say I use a sulfate free shampoo (Kiss My Face Whenever Shampoo) and no conditioner (I didn't need it when I had a pixie and now that I have a bob, spacing out my shampooing has been enough to keep my undyed hair healthy) or styling products, so I don't have to deal with build up.