We present measurements of branching fractions and charge asymmetries for the decays B-->etaK*, where K* indicates a spin 0, 1, or 2 Kpi system. The data sample corresponds to 344x10(6) BB pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+ e- collider at SLAC. We measure the branching fractions (in units of 10(-6): B(B0-->etaK*0(892))=16.5+/-1.1+/-0.8, B(B+-->etaK*+(892))=18.9+/-1.8+/-1.3, B(B0-->eta(Kpi)0*0)=11.0+/-1.6+/-1.5, B(B+-->eta(Kpi)0*+)=18.2+/-2.6+/-2.6, B(B0-->etaK2*0(1430))=9.6+/-1.8+/-1.1, and B(B+-->etaK2*+(1430))=9.1+/-2.7+/-1.4. We also determine the charge asymmetries for all decay modes.