Should I use a moisturizer even if I have oily skin?

Yes. Oily and combination skin still have areas needing moisturizer such as the eyes and lips. Oily skin uses lighter lotions or serums as opposed to heavier creams for dry skin. Also many products typically used on oily skin such as glycolic acid or Retin-A or retinol can cause some irritation of the skin which can be calmed with moisturizers.