Polarized Raman measurements are performed on oriented single crystals of PdO, grown by a vapor-transport technique. The allowed Raman modes, B1g and E(g), are assigned to lines at 651 and 445 cm-1, respectively. Intensity-versus-excitation-wavelength profiles for these lines show a strong resonance behavior, the presence of which leads to the appearance of numerous additional features in the spectrum. By fitting these profiles to an exciton model of resonant Raman scattering we obtain HBAR-omega-ex = 2.423 +/- 0.011 and HBAR-GAMMA = 0.071 +/- 0.018 eV for the exciton energy and half-width. Both the position and width match well a prominent peak in Im(epsilon) appearing in the PdO optical properties reported by Nilsson and Shivaraman [J. Phys. C 12, 1423 (1979)]. Phonon-dispersion curves and the density of states are calculated with a simple valence-force model incorporating the important bond-stretching and -bending motions. With these calculations and with results from experiments on isotopically substituted (PdO)O-18, we are able to assign most of the additional features in the Raman spectrum to second-order scattering from overtones and combinations or to forbidden LO-phonon scattering. The overtone of the B1g mode appears as a sharp line in the spectrum, very similar to the case for the single Raman-active mode in diamond.