The best solution is the simplest: If you see an oil slick forming in the skimmer, ladle it out into a bucket and then pour it down the drain.
You don't want to use chemicals. That would only cause the oils to mix with the water, which is not where you want them.
There are about ten reasons why you should aerate the pool. When you start aerating, you will be amazed at the amount of oil that comes to the surface. There is a proverb that says oil and water don't mix, and they don't mix very much, but 30,000 gallons of water will hold an impressive amount of oil. The oil sticks to the surface of the aerator bubbles and comes to the surface. Run the aerator and skimmer together, and ladle out the oil as mentioned above.
There are two kinds of oil. The fats and oils that come from plants and animals contain so-called fatty acids, such as oleic acid, palmitic acid, stearic acid, et cetera. Soaps also contain fatty acids. If such things get into the water, they will react with calcium to form calcium stearate et cetera. You've seen that before in the form of hard waxy or greasy soap scum that forms in the bathtub or shower. If a "bathtub ring" forms around the edge of the pool, just scrape it off and throw it away. The chemicals you might use for cleaning the bathtub are not suitable, because they depend on rinsing out the tub, and you can't do that in the pool.
The other type of oils are like motor oil or vaseline. They are much less reactive.
Yes, oil will stick to the DE in a DE filter. It exits the system when you replace the DE. This works OK if there is a tiny amount of oil, but for larger amounts it is woefully inefficient.
Similarly, oil will stick to the sand in a sand filter. This is much more of a problem. Cleaning the sand is a pain, and replacing the sand is an even bigger pain. I feed a little bit of DE into my sand filter every so often, in hopes that the oil will preferentially stick to the DE, and exit the system at the next backwash. However, mostly I just try to keep oil out of the filter. If there is an oil slick in the skimmer I do *not* allow it to get sucked into the filter. I ladle it out.