At what temperature will the fats on meat render

To store fats, you should always use glass as plastics react to fats by absorbing some and perhaps discoloring or transferring flavors to your fat. Depending on use, I prefer to work with cold fat at the start as it has a much broader possible use and I don't like to wait when I make biscuits, so I keep mine in the fridge. However, you gain very little extra life out of keeping it in the fridge and if you don't keep it in a sealed container you run a very real risk of flavor transference there to. If you don't make pastry dough or other such, your counter top is a perfectly acceptable place to store, as long as you use it up before it goes rancid. One thing to keep in mind is that fats can sometimes have very different shelf lives, so make sure you taste or smell before use, regardless of storage method.

I don't think there's any dairy in twinkies or similar packaged items -- it's whipped fat, with sugar and flavorings.

But all of the items you mention contain fat, so it's possible that it's a product of rancidity.

I don't know if it's related to the supertasters stuff that bikeboy389 mentioned, but some people experience taste differently -- I can't stand bitter flavors (about 1/2 the items on the list mentioned, especially coffee, artificial sweeteners and all hopped beers), but I love sour; much more so than most other people. People also smell differently (eg, the issue with asparagus, although that one's an issue not just with sensing it), so it's possible that you're just more sensitive to taste/smells in general, or to a specific chemical compound than others.