I keep coconut, olive oil and lard in our pantry. The other oils and butters like shea, pko, avocado, almond, castor, etc are kept in a small cupboard that I use for only soaping oils. I have a few small bottles of fancier stuff like hempseed, macadamia nut, walnut; things I see in my travels and want to try as extras, but don't usually use as part of a recipe. Those are in the oil cupboard now, in a dark bin, but I thinking they may be going into the fridge just for safety. It's cold in the house now, but come spring it'll warm up and I don't want them to go off.
I just moved the majority of my soapy stuff upstairs to our guest/craft room. That's where the fragrance and essential oils are, in bins, in alpha order. I keep additives and things up there too; only molds, blender, thermometer, scale, spatulas, etc are downstairs now. My routine is to choose a recipe, measure out oils, go upstairs and get add-ins and a scent, and then only what I'm using for that batch is on the soap counter. Feels less chaotic and more organized that way.