The spin-density-wave (SDW) states of a quasi-one-dimensional system with an incommensurate wave vector perpendicular to the chain have been studied in the presence of two kinds of commensurate potential, which originate in a quarter-filled band and under dimerization along the chain. For the phase variance phase of the SDW order parameter, we classically treat a two-dimensional Hamiltonian, which includes both acoustic excitation with a long wavelength and a vortex excitation with a short wavelength. A phase diagram on the plane of temperature and chemical potential (where the latter corresponds to the deviation of the transverse wave vector from the commensurate one) exhibits a variety of states given by the commensurate SDW state without charge density, the commensurate SDW state with charge density, the incommensurate SDW state, and the disordered state.