What is the best method of storage for condiments?
To a certain extent, it depends on the condiment.

For things like oil or vinegar, where germs generally can't really survive anyway, there is no need for refrigeration. On the other hand, things like ketchup, mayonnaise, or any other emulsions (tahini for instance) should be kept in the fridge.
It also depends on whether the pack is sealed or has come into contact with air already. For example, sealed packs of mayonnaise can be kept at room temperature, though an open jar must be refrigerated.

Aside from that, it's always a good idea to keep things in sealed containers, and away from direct sunlight.