I have used a couple different types, like Mr. Laredo, MCT Oil by Twinlab a long time ago, and am now taking organic Coconut Oil (for awhile) which has been great!
I don't refrigerate the Coconut Oil because it is already pretty dense/thick, and it hardens too much when it gets cold. I haven't had any problems with the Coconut Oil.
I don't see where it would hurt to refrigerate the oil, as far as moisture goes, as long as you keep the lid tight. And when you take it out of the fridge, don't leave it sitting around for long periods of time with the lid open and you shouldn't have any mositure problems.
I don't know what kind you have, but if it ever gets a little too thick, you can always set it in a glass of warm water for several minutes before taking. That's what I do occcasionally. Hope that helps bro.