For makeup, you need to avoid products with silicone, oil, waxes. They make you sweaty and oily. Also avoid bismuth oxychloride and things with sparkles because they bring attention to oil.
You need a magnesium silicone and oil free based primer to best control oil. Becca's Ever Matte is the best one if willing to splurge, Mehrons Antishine gel if on a budget.
Use powder foundation and makeup as much as possible as it best works with oily skin and avoid ones again with silicones, oils, waxes, etc... Mineral powders like Ella Rose Minerals, Alima Pure, Lucy Minerals, Faerie Organic, Aromaleigh, LA Minerals, Everyday Minerals, Meow Cosmetics, Dreamworld Hermetica, etc all have awesome formulas for oily skin and you can get light to full coverage depending on how you apply. If you apply wet and/or with flat top brushes like sigma's f 80 you can get medium to full coverage. You can use a concealer brush to concentrate a powder foundation like concealer. You can also get good multipurpose powder concealers like Ella Roses MSM concealer.
If you want to use a finishing translucent powder or use it without foundation/concealer etc, get Mattify! Cosmetics Ultra. It is the best powder for oil control.
If you use blush, bronzer, illuminator, etc... try to go powder or at least oil and silicone free if not powder.
Use a finishing spray that actually works to lock in makeup. Don't get the drugstore ones or the urban decay etc they don't work. Get ones formulated specifically for film and stage and heavy duty cosplay. Get one from ben nye or kryolan, they work in all these scenarios and will work in day long oily skin scenarios.
Now for skincare... get a cleanser for oily/combo skin, use baking soda as a scrub a few times a week, use witch hazel as toner and don't use oil as a moisturizer. use something aloe based as it will leave a matte finish but hydrate your skin not over dry it. Use spf with that too if possible instead of a greasy one.
You can also talk to a dr about overly oily skin. Sometimes birth control will help with hormonal imbalances that cause oily skin. if that doesn't work, acutane to also treat acne and stop oil production. however, if you do acutane, you must always no matter what stay out of the sun or wear a lot of sunscreen you reapply or wear a sunhat anything to shield yourself because it makes you very very sunburn prone and you will need to drink a lot of water and moisturize then because it can make skin a little too dry.