The ω-, ϱ-, and φ-resonance production and their dileptonic decay in π-A reactions at 1.1-1.7 GeV/ c are calculated within the intranuclear cascade (INC) approach. The invariant mass distribution of the dilepton pair for each resonance can be decomposed in two components which correspond to their decay "inside" the target nucleus and in the vacuum, respectively. The first components are strongly distorted by the nuclear medium due to resonance-nucleon scattering and a possible mass shift at finite baryon density. These medium modifications are compared to background sources in the dilepton spectrum from πN bremsstrahlung as well as the Dalitz decays of ω and η mesons produced in the reaction. Detailed predictions for π-Pb reactions at 1.3 and 1.7 GeV/ c are made within several momentum bins for the lepton pair.