The interference of electromagnetic and weak production mechanisms for lepton pair production may give rise to several effects which violate parity and charge symmetry. These effects are generally of the order of 1% for dilepton masses of 10 GeV. The theoretical calculations presented here show that experimental studies of these asymmetries may be useful. In particular, measurements of these asymmetries in collisions of pions with polarized protons may lead to a greatly enhanced understanding of the polarization distribution of quarks in a polarized proton. The polarization structure of the d quark is shown to be of special interest. Measurement of the parity-violating asymmetries in proton-polarized proton collisions may prove to be a sensitive probe of the flavor symmetry of the proton antiquark sea. Analysis of the parity conserving charge asymmetry (which is predicted to occur in collisions of unpolarized hadrons) allows a unique further test of the Drell-Yan model for lepton pair production, as well as of our understanding of weak interactions. The above asymmetries mentioned are computed within the framework of the parton model. The focus of this work is on the asymmetries calculated with the inclusion of first-order perturbative QCD effects. The asymmetries are calculated in a differential form for values of the dilepton transverse momentum large compared with the typical (∼1 GeV) scale of nonperturbative effects, and also in a form in which this transverse momentum has been integrated over. Corrections to the parton model results, which can be large, show rather different structure for the various asymmetries. A parity-violating asymmetry which may occur in collisions of unpolarized hadrons is also discussed. This asymmetry is very sensitive to the nonperturbative structure of hadrons, and is estimated to be approximately 0.01% for dilepton masses of 10 GeV.