Depends on what kind of oils you're talking about, how you're using them, and what you're using them for.
That's what I was going to say. Also, is your fur-baby canine or feline? Felines can't metabolize medium-chain fatty acids like coconut oil, but dogs might be okay with it. DeeDee is our resident dog expert.
Basically, if you give a good fish oil, something like Nordic Naturals salmon oil, that has a lot of Omega 3s, that's better than a vegetable oil. Omega 3s are anti-inflammatory.
I hope this helps, and welcome!