  We report measurements of branching fractions and CP asymmetries for $B \to
\eta K^*$ and $B \to \eta \rho$ decays. These results are obtained from a $414
{\rm fb}^{-1}$ data sample collected at the $\Upsilon(4S)$ resonance with the
Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We measure the
following branching fractions: ${\mathcal B}(B^0 \to \eta K^{*0}) = (15.2 \pm
1.2 \pm 1.0)\times 10^{-6}$ and ${\mathcal B}(B^+\to\eta K^{*+}) =
(19.3^{+2.0}_{-1.9}\pm 1.5)\times 10^{-6}$, where the first error is
statistical and the second systematic. We also find a $2.7\sigma$ excess in the
$B^+\to\eta \rho^+$ mode and measure $\mathcal B(B^+\to\eta \rho^+)=
(4.1^{+1.4}_{-1.3}\pm 0.4)\times 10^{-6} <6.5 \times 10^{-6}$ at 90% confidence
level. For $B^0 \to \eta \rho^0$ decays, we determine the upper limit $\mathcal
B(B^0\to\eta \rho^0) < 1.9 \times 10^{-6}$ at 90% confidence level. The partial
rate asymmetries are ${\mathcal A_{CP}}(\eta K^{*0}) = 0.17 \pm 0.08 \pm 0.01$,
${\mathcal A_{CP}}(\eta K^{*+}) = 0.03 \pm 0.10 \pm 0.01$, and ${\mathcal
A_{CP}}(\eta \rho^+) = -0.04^{+0.34}_{-0.32}\pm 0.01$.
