We present measurements of B-meson decays to the final states η′ρ, η′f0, and η′K*, where K* stands for a vector, scalar, or tensor strange meson. We observe a significant signal or evidence for η′ρ+ and all the η′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 467×106 BB̄ 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 K2*(1430) with respect to the vector K*(892) component. © 2010 The American Physical Society.