When I first started OP'ing, I was using extra-virgin olive oil. It took a little over a month before my skin was less oily. I stopped pulling for a while and my oily skin came right back. I pulled with soybean oil with okay results.
Once I started using coconut oil (I started first two weeks of this month), my oily skin went away. I stopped washing my face with soap months ago. I use an apricot scrub when I clean my face. I only use this 2 times a day. This also helps to keep my skin from getting oily.