Unique means “one of a kind.” There are no degrees of uniqueness: something is unique, or it is not. If you want a word that admits degrees, use special or unusual.
Usage is a guide on how to use something properly; use means “one or more instances of using something,” or “function.” Thus the use of a semicolon is to separate clauses, while its usage is the list of rules on exactly how it has to be used. Someone who knows the use of a word understands how it fits in a sentence; someone who knows the usage has studied the grammatical rules, semantic relations, and appropriate mechanics. Each time you use something, that's one use (the noun), not one usage. Unless you're talking about grammar, you usually mean use rather than usage: don't use the longer word just because it sounds more impressive. [Revised 14 July 2000]
Use is almost always better, whether pronounced yooz as a verb or yoos as a noun. Don't longwordify what would otherwise be clear.