© 2015 American Physical Society. We report on the first observations of B¯0→D1(2430)0ω, B¯0→D1(2420)0ω, and B¯0→D2∗(2460)0ω decays. The B¯0→D∗+ρ(1450)- decay is also observed. The branching fraction measurements are based on (771.6±10.6)×106 BB¯ events collected at the (4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. The fractions of longitudinal polarization of the D∗∗ states as well as partial wave fractions of the D1(2430)0 are obtained. We also set a 90% confidence level upper limit for the product of branching fractions of B(B¯0→D∗+b1(1235)-)×B(b1(1235)-→ωπ-). The measurements show evidence of nontrivial final-state interaction phases for the ρ-meson-like amplitudes.