I noticed a difference after cutting out oils in about a week or so...a dramatic difference in two weeks and my skin really improved after a month of no oils and the residual clogged pores had cleared out. I also use meds (see below) but they never got me completely clear, even after years and years of use. Same with diet changes until I avoided the oils. I get monthly microdermabrasions that help unclog pores but like the meds, they never got me completely clear...however I think that after stopping oils the microdermabrasions work even better --- and the clinicians who do them agree.
Avoiding oils means avoiding all foods that have added oils in them...like foods fried in oil, etc. Foods that naturally have oils such as avocados are good to eat since the body knows how to use those oils without becoming inflammed. It is the processed oils that are a problem...the body was not designed to use those oils very well and people prone to inflammation especially.
The key thing I notice is that avoiding oils changes the quality of the sebum...makes it less sticky and less of it --- so less clogging and less inflammation.
I avoid bread not because I am gluten sensitive but there is something else in bread that seems to inflame my skin. I can eat pasta once a week or a burrito no problem so all I can think is that the yeast used in bread is an issue. Also bread is usually made with oils and sugars which both are problems for me. Whole wheat bread is the very worst for me...same with whole wheat pasta...but white pasta or burrito shells are okay. Go figure...whole wheat is supposed to be so wonderful but not for me! I've looked into gluten-free breads but they are loaded with sugars and oils and so don't work. And gluten-free burrito shells are awful. I do eat brown rice pasta and actually like it but it is made with straight forward brown rice flour...no sugars or oils.
I take Opti-L Zinc, Citrical + D, an organic multi, and Multi-Flora Probiotic. This probiotic is very expensive but it has really made a difference in improving my digestion. I also eat tons of vegies, berries and tubers (potatoes, yams), and small amounts of free-range eggs and fowl, and wild fish. My diet somewhat mimics those of cultures that don't get acne and is what is called "nutrient dense".
Thanks so much for replying! Its hard to cut off oils, but I need to try it out to notice a difference like you did. Its more difficult when I don't cook much. Its time I learned healthier options. Thanks again 
What kind of oils have you cut out? I find that vegetable oil, canola oil, and hydrogenated fats all cause breakouts, but olive oil, coconut oil (organic, non-hydrogenated), butter, ghee, lard (non-hydrogenated), are excellent for health. I wouldn't cut out all oils, just rancid, hydrogenated, processed oils.
Your body needs fat to absorb nutrition effectively.
I cut out all processed oils except for a tiny amount of organic EVOO when cooking. All other oils seem to cause problems for me. The research I did indicated most oils in use today are made with artificial solvents. People traditionally did not consume them because they were impossible to make before industrialization.
Butter, ghee and lard have been used traditionally but I find them hard to digest (even ghee). Butter and ghee are dairy and since they are concentrated from milk, they also have concentrated amounts of the hormones inherent naturally in dairy products. These hormones can cause problems for acne prone people. Ghee may be a wonderful food for non-acne prone people but I'm not so sure for people like me. Lard is one of the hardest things for me to digest...it is so thick.
Many people seem to do okay with coconut oil but you have to be sure it is pressed and not made with solvents.
Personally for me it is more an issue of added fat --- too much and the oil in my pores seems to get stickier and more abundant thus clogging them up more easily. I've noted that if I avoid processed oils then my skin is much much less oily and if I do get a clogged pore or teeny whitehead it clears out in a day...whereas before I would get inflammation and a raised small pimple that would last days. And years ago when I ate lots of oils I got cystic acne (not fun).
There is plenty of oil in vegetables, especially if you eat avocados, etc. And whole grains have oil in them too. These oils are naturally part of the foods, incorporated in ways we may not yet fully understand (...kind of like the issue with consuming isolated vitamins in suppliments versus eating whole foods...). The body knows how to digest and use these oils because this is how people got their oils for eons. It seems to me that the more we can eat a minimally processed diet the better our bodies will function. And I have experienced this firsthand. I firmly believe mother nature knows what we need and whole foods provide it.
If you're eating coconut or olive oil (both of which were consumed by traditional cultures) I imagine it would be best to eat them the way our ancestors did...very very sparingly. Oil is a hard thing to make by hand and so it was very precious. Traditional cultures did not consume the quantities of oil that people do today. Can you imagine pressing olives by hand to get eneough oil to cook with...a long process. Or what about coconuts? Same thing. The oil produced would be precious.
Some people benefit from eating more fruit but if your acne is affected by sugars then avoiding high-fructose fruits like citrus (oranges) is helpful (...also high-fructose vegetables such as carrots...). Also if your acne has a bit of rosacea involved in it...which often is the case with adult acne...then avoiding citrus fruits helps because citrus is one of the triggers for rosacea, especially acne-rosacea (papular-pustular rosacea). However there are many fruits that are not as high-fructose such as berries and a little bit of banana. Berries and banana are often tolerated by people sensitive to high-fructose. I am one of those people and my acne is always better if I stick to berries and a bit of banana...not too much though!