  We discuss phase transitions and the phase diagram of a classical dimer model
with anisotropic interactions defined on a square lattice. For the attractive
region, the perturbation of the orientational order parameter introduced by the
anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a
dimer-liquid to columnar phases. According to the discussion by Nomura and
Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we
proffer criteria to determine transition points and also universal
level-splitting conditions. Subsequently, we perform numerical diagonalization
calculations of the nonsymmetric real transfer matrices up to linear dimension
specified by L=20 and determine the global phase diagram. For the repulsive
region, we find the boundary between the dimer-liquid and the strong repulsion
phases. Based on the dispersion relation of the one-string motion, which
exhibits a two-fold ``zero-energy flat band'' in the strong repulsion limit, we
give an intuitive account for the property of the strong repulsion phase.
