Oils can be fragile and turn rancid easily, it depends on the oil. Flax oil is very fragile and should be kept cool. I kept mine in the frig. and the store I bought it from also kept it in a refrigerated unit along with all their flax meal and seeds.
I use olive oil for most things. I keep both the extra virgin and the regular. The one thing I haven't paid much attention to is keeping my oil fresh and protecting it from heat. It is not so fussy but still can go rancid if abused. I buy those big bottles at Costco and I think I'm going to be more careful about buying more than I can use in a reasonable time and keep it is an opaque container, like the photo, away from heat.
I have a small bottle of macadamia nut oil that is suppose to be pretty stable but I do keep it in the frig because I don't use it very often. It's kind of expensive, but being I have it I want to start using it for a salad or a finishing oil.
Walnut oil is good for the same thing. Because I don't use butter anymore I could use one of these oils on vegs. in the same way you would use butter. The reason for this is to get their benefits and be able to taste their delicate flavors. I had a bottle of Roasted Walnut oil that had gone rancid because I let it sit too long, so I got rid of it. It is used in French cooking. I'll have to check out how they use it.
Grape Seed oil is considered good by some people. I have a bottle of it in my frig. because some of the recipes I use call for it, but I may reconsider if I want to continue to use it. The information I read about it was that it could have an oxidation problem if you use high heat like frying as some people use it, but I don't do that so I'm not sure about this one. It is expensive and that may be a good enough reason to find something else to use like the lighter olive oil.
A food that contains healthy oil is avocado and I want to include more of those in my diet. I saw a recipe from the veggie nook for pesto using kale and avocado. The avocado replaces the oil. Sound interesting. I'll have to try that this week with spaghetti squash. You can also get avocado oil. I want to look into this because sometimes avocado's don't appeal to me. WHF has a page on avocado.
I'm also going to restart taking my fish oil. It is suppose to be the best way of getting your omega 3's. Flax is another source but your body has to convert it and that doesn't work as well. It is used more by vegetarians. Here is an article by WHF on omega 3's and what they do for you.
Coconut oil is the best if you're not afraid of saturated fats. It's very healthy. One of the problems with it for me is it causes digestive upsets until you get use to it. So I stopped using it and am not well enough to go back to it yet. My healing process has been slow.
Mark's Daily Apple had some good information on oils from his prospective and I like what he has to say.