We report on the first observations of (B) over bar (0) -> D-1 (2430)(0)omega, (B) over bar (0) -> D-1 (2420)(0)omega, and (B) over bar (0) -> D-2* (2460)(0)omega decays. The (B) over bar (0) -> D*(+) rho(1450)(-) decay is also observed. The branching fraction measurements are based on (771.6 +/- 10.6) x 10(6) B (B) over bar events collected at the Upsilon(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 D-1 (2430)(0) are obtained. We also set a 90% confidence level upper limit for the product of branching fractions of B((B) over bar (0) -> D*(+)b(1) (1235)(-)) x B(b(1) (1235)(-) -> omega pi(-)). The measurements show evidence of nontrivial final-state interaction phases for the rho-meson-like amplitudes.