I think Jeff is right to point out that they are all grammatically correct; all the phrases you have given are perfectly valid and clear in meaning.
Where I would disagree with both Jeff and Nicholas is in preferring 3 and 4 to 1 and 2, where I believe the opposite to be the case.
Deterrence is a very general and abstract noun. Its use is quite rare, and only justified here via relatively obscure grammatical reasoning.
Deterrent is both a concrete noun, describing something which is believed to deter (e.g. an H-bomb), and an adjective describing such a thing. There are many words which are etymologically adjectives, such as detergent, emollient, stupefacient, etc., which have a similar double life as nouns. We regularly use soap for its detergent properties, coconut for its emollient effect, a large dog for deterrent purposes; it's 1 and 2 all the way.
Looping back to what deterrence means, as a noun it describes the deterrent power/quality that a deterrent posseses. Deterrence theory would be the theory of such powers.
Your second question seems to describe the opposite of deterrence theory, which holds that nukes deter (i.e. prevent) violence. The theory may or may not be true.