  We describe searches for B meson decays to the charmless vector-vector final
states omega K* and omega rho in 89 million B-Bbar pairs produced in e+e-
annihilation at sqrt(s)=10.58 GeV. We measure the following branching fractions
in units of 10^{-6}:
  BF(B0 -> omega K*0) = 3.4 +1.8 -1.6 +/- 0.4 (<6.0),
  BF(B+ -> omega K*+) = 3.5 +2.5 -2.0 +/- 0.7 (<7.4),
  BF(B0 -> omega rho0) = 0.6 +1.3 -1.1 +/- 0.4 (<3.3), and BF(B+ -> omega rho+)
= 12.6 +3.7 -3.3 +/- 1.6. The first error quoted is statistical, the second
systematic, and the upper limits are defined at 90% confidence level. For B+ ->
omega rho+ we also measure the longitudinal spin alignment fraction f_L = 0.88
+0.12 -0.15 +/- 0.03 and charge asymmetry Ach = (5 +/- 26 +/- 2)%.
