In-medium interactions of $\omega$-mesons in infinite nuclear matter and finite nuclei are investigated in a microscopic approach with $N^{-1}$ and $N^*N^{-1}$ particle-hole polarization modes including $N^*$ resonances. The nuclear polarization tensor formalism is used. Covariant mean-field self-energies are taken into account. Longitudinal and transversal self-energies are derived. The theoretical results is applied to finite nuclei in local density approximation. Applications to recent data on the in–medium width of $\omega$ mesons in $^{93}Nb$ are presented. The data are well described by self–energies containing S-wave and P-wave $N*$ resonances. Low-energy parameters are determined. For the first time a spectrum of omega-nucleus bound states is obtained, albeit with reduced lifetimes.