We describe searches for B meson decays to the charmless vector-vector final states ωK*, ωρ, ωω, and ω with 233×106 BB̄ pairs produced in e+e- BB̄ annihilation at s=10.58GeV. We also search for the vector-scalar B decay to ωf0. We measure the following branching fractions in units of 10-6: B(B0→ω K*0)=2.4±1.1±0.7(<4.2), B(B+→ωK*+)=0.6- 1.2-0.9+1.4+1.1(<3.4), B(B0→ωρ0)=-0.6±0.7-0.3+0. 8(<1.5), B(B+→ωρ+)=10.6±2.1-1.0+1.6, B(B0→ωω)=1.8-0.9+1.3±0.4(<4.0), B(B0→ω)=0. 1±0.5±0.1(<1.2), and B(B0→ωf0)=0.9±0.4-0.1+0. 2(<1.5). In each case the first error quoted is statistical, the second systematic, and the upper limits are defined at the 90% confidence level. For B+→ωρ+ decays we also measure the longitudinal spin component fL=0.82±0.11±0.02 and the charge asymmetry ACP=0.04±0. 18±0.02. © 2006 The American Physical Society.