Quantum transport through single molecules is essentially affected by molecular vibrations. We investigate the behavior of the prototype single-level model with weak to intermediate electron-vibron interactions and arbitrary couplings to the leads. For this, we have developed a nonequilibrium self-consistent theory which allows us to explore the nonperturbative regime via the nonequilibrium Green function formalism. We show that the nonequilibrium resonant spectroscopy is able to determine the energies of molecular orbitals and the spectrum of molecular vibrations. Our results are relevant to scanning tunneling spectroscopy experiments and demonstrate the importance of the systematic and self-consistent investigation of the effects of the vibronic dynamics onto the transport through single molecules.