An ab initio based theoretical approach to describe nonequilibrium many-body effects in molecular transport is developed. We introduce a basis of localized molecular orbitals and formulate the many-body model in this basis. In particular, the Hubbard-Anderson Hamiltonian is derived for single-molecule junctions with intermediate coupling to the leads. As an example we consider a benzenedithiol junction with gold electrodes. An effective few-level model is obtained from which spectral and transport properties are computed and are analyzed. Electron-electron interaction crucially affects transport and induces multiscale Coulomb blockade at low biases. At large bias, transport through asymmetrically coupled molecular edge states results in the occurrence of "anomalous" conductance features, i.e., of peaks with unexpectedly large/small height or even not located at the expected resonance energies.