I have oily skin, too. My foundations don't feel tacky. Even when we seem the same what works varies so what I do may or may not work for others...
I always use a primer first, over skincare & before makeup - I use Monistat (not sold as a primer but works great as one) or Spackle mattifying oil control primer.
I don't care for liquid foundations & find that creams or powders work best for me. Cover Girl/Olay Simply Ageless & Laura Geller Balance and Brighten are examples of foundations I use & like. I always finish with Mally Poreless Face Defender to help my makeup last through the day.
Are you using any skincare serums during the day? Sometimes they can leave skin feeling tacky if too much product is used or it is not given enough time to absorb/set.