Do postdocs in the United States generally get annual raises? Do postdocs in the United States get raises in general? (Is this different for postdocs hired under specific grants vs postdocs hired through departments, such as in mathematics?) If there are raises, how are they determined?
From my experience in the US, it is typical for a postdoc to be on a fixed "short term" contract where there are certainly no "promotion" raises, but might or might not provide cost-of-living increases.  

A one-year contract will almost certainly contain no salary increase; for a 2- or 3-year contract, they will be minimal at best.