We present measurements of B meson decays to the final states omegaK*, omegarho, and omega f_0, where K* indicates a spin 0, 1, or 2 strange meson. The data sample corresponds to 465x10^6 BBbar pairs collected with the BABAR detector at the PEP-II e+e- collider at SLAC. B meson decays involving vector-scalar, vector-vector, and vector-tensor final states are analyzed; the latter two shed new light on the polarization of these final states. We measure the branching fractions for nine of these decays; five are observed for the first time. For most decays we also measure the charge asymmetry and, where relevant, the longitudinal polarization f_L.