I don't refrigerate my oils. I do but them in a dark colored bottle and place them in the back of my closet where it is cool and dark. I never store any of my oils in my kitchen cabinets or laundry area.
If you have a small cottage styled home like I do :-), space is limited. I bought colored plastic bins to store my bottles of oil in my shed outside (in the winter time). In the summer time, I put my winter clothes in shed. It works!
I freeze my Hemp, Avocado, Emu and Neem oils because these are oils that are not part of my regular oil rotation. Therefore they tend to hang around longer than others. As for my essential oils I keep those in a cool dark cabinet.
I store my essential oils in a cool dark space in a small glass curio cabinet which I painted. They look beautiful! Out of sunlight . Ofcorse. And in amber bottles. I buy large but transfer to 1/2 oz. bottles so that the larger bottles stay closed for long periods of time not allowing air in. And did I say that my collection looks beautiful. Large bottles stay stored in the dark . I am using up the smaller bottles , than refilling.
I keep my eo's in plastic bins in an extra refrigerator I have. If you don't have this luxury, then a cool place is fine. I keep my jojoba in my basement that stays cool and I do freeze my shea butter to extend shelf life.
You should refrigerate your citrus peel oils (not the ones that have been distilled) as they oxidize quickly. It's best to keep those bottles as full as possible. Amber or colored glass does NOT prevent UV radiation from degrading oils. I also refrigerate my absolutes and CO2 extractions, since they are subject to oxidation as well.