We consider charge transport through a nanoscopic object, e.g. single molecules, short nanotubes, or quantum dots, that is weakly coupled to metallic electrodes. We account for several levels of the molecule/quantum dot with level-dependent coupling strengths, and allow for relaxation of the excited states. The current-voltage characteristics as well as the current noise are calculated within first-order perturbation expansion in the coupling strengths. For the case of asymmetric coupling to the leads we predict negative-differential-conductance accompanied with super-poissonian noise. Both effects are destroyed by fast relaxation processes. The non-monotonic behavior of the shot noise as a function of bias and relaxation rate reflects the details of the electronic structure and level-dependent coupling strengths.