How do you manage your oily-dehydrated skin?

I didn't know what "dehydrated oily skin" was until I came here. After looking into it, it seems I do have it. I thought I had oily skin, but it turns out I'm the type where the skin underneath is dry. Since my skin is oily and gets shiny and greasy, I used to skip applying lotion and cream, but I think that actually made the dryness worse. I am applying them properly these days, but sometimes I only use cream because of sweat. That shouldn't be the case, right? Do other people with dehydrated oily skin take good care of their skincare routine? What would be good to use?