Hi, Matt-
(Sidenote: "Paul", please, instead of "Dr. Taylor".)
3dresample can be used to adjust lots of dataset and header properties together---it assumes that things are correct to start with (in contrast to 3drefit, which is used to fix/change just header info, leaving the data unchanged).
You can resample to a new grid, yes, that is typically something that 3dresample is used for. After that, your dataset might still appear in the same spatial (xyz) location, but have different orientation or voxel size or matrix size or... something.
I don't know that matrix dimensionality even/oddness is a requisite in AFNI---a benefit of even matrix sizes is that the left and right hemispheres can be easily split, rather than having a "zero" slice that is neither, for example.
--pt