Strings come in a range of sizes, from 0.08-0.38 to 0.14-0.56. I would recommend that for a guitar with a whammy bar you use a lighter/thinner set of strings. this is because the tension is a lot weaker which will allow the whammy bar to sit in place comfortably. Heavier strings are a lot stronger in tension and can put the whammy bar out of place when your guitar is in E Tuning.
If you really do want to have a thicker set of strings, because it gives a chunkier tone, I would only recommend that it be used with a guitar that does not have a tremolo bridge. Therefore the string tension will not be altered by the pull on the whammy bar, meaning your guitar won't go out of tune quickly.
(The two guitars on the left work better with thinner strings. The two on the right are capible with thick and thin strings)