An analysis of the high resolution optical spectra (10 and 300 K) of the self-stimulated Raman scattering active Nd:SrWO4 crystal was performed. Crystals doped only with low concentrations of Nd or codoped with Na+ or Nb5+ grown in N2 or air atmosphere were investigated. The single Nd-doped crystals show five main centers, whereas codoping with Na+ in the ratio Na/Nd=3/1 (in melt) simplifies considerably the spectra. Codoping with Nb5+ does not lead to a dominant center and introduces a new one. Growth in air revealed the role of the oxygen in the charge compensation and multicenter structure of the spectra. The spectral characteristics of the nonequivalent centers (levels, intensities, and polarization) function on concentration of Nd3+ and of codoping ions and growth conditions were analyzed. The polarization data show that only one center has ideal local symmetry S4. Based on the crystal structure, previous results, and the new spectral data, an attempt to connect various spectral nonequivalent centers to the charge compensators (Sr2+ vacancies, interstitial oxygen, Na+, and Nb5+) is made and structural models for various centers are proposed. The implications of these findings on the laser emission characteristics and on the selection of the pumping transitions are also discussed.