We present measurements of B-meson decays to the final states eta'rho, eta'f(0), and eta'K*, where K* stands for a vector, scalar, or tensor strange meson. We observe a significant signal or evidence for eta'rho(+) and all the eta'K* channels. We also measure, where applicable, the charge asymmetries, finding results consistent with no direct CP violation in all cases. The measurements are performed on a data sample consisting of 467 X 10(6) B (B) over bar pairs, collected with the BABAR detector at the PEP-II e(+)e(-) collider at the SLAC National Accelerator Laboratory. Our results favor the theoretical predictions from perturbative QCD and QCD factorization and we observe an enhancement of the tensor K(2)*(1430) with respect to the vector K*(892) component.