We present the results of a study of the charmless vector-vector decay B-0 -> omega K*(0) with 657 X 10(6) B (B) over bar pairs collected with the Belle detector at the KEKB e(+)e(-) collider. We measure the branching fraction to be B(B-0 -> omega K*(0)) = [1.8 +/- 0.7(stat) +/- 0.3(syst)] X 10(-6) with 3.0 sigma significance. We also perform a helicity analysis of the omega and K*(0) vector mesons, and obtain the longitudinal polarization fraction f(L)(B-0 -> omega K*(0)) = 0.56 +/- 0.29(stat)(-0.08)(+0.18)(syst). Finally, we measure a large nonresonant branching fraction B[B-0 -> omega K+ pi(-); M-K pi is an element of (0.755, 1.250) GeV/c(2)] = [5.1 +/- 0.7(stat) +/- 0.7(syst)] X 10(-6) with a significance of 9.5 sigma.