Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Does the (irregular) space-filling octahedron meet your criteria? (The tiles are not all obtained from a single tile by translation, i.e., this is not a lattice tiling. Instead, there are three families of mutually-orthogonal tiles in a tessellation.)

No. The body-centered cubic tetrahedron tiles it as well.

Please note that an isohedral polyhedron is not just a polyhedron in which all faces are congruent, but one in which all the faces also lie in the same symmetry orbit (which unfortunately is not the case for the irregular space-filling octahedron).