Absolute state-selected cross sections for the reactions O+(S-4,D-2,P-2)+N-2-->N-2(+)+O,NO++N, and N++NO (and/or N++N+O) have been measured in the center-of-mass collision energy (E(c.m.)) range of 0.06-40 eV employing the differential retarding potential method and the O+(D-2) and O+(P-2) ion state-selection schemes we developed recently. Charge transfer is the overwhelming product channel for the O+(D-2)+N-2 and O+(P-2)+N-2 reactions. Contrary to the results of previous experiments, the charge transfer cross sections for O+(P-2)+N-2 are found to be 30%-100% greater than those for O+(D-2)+N-2. This observation suggests that N-2 is an excellent quenching gas for O+(D-2,P-2). While the E(c.m.) dependencies for the cross sections of NO+ from O+(S-4)+N-2 and O+(D-2)+N-2 are similar, exhibiting a broad maximum in the E(c.m.) range of 1.5-8 eV, the cross section for NO+ from O+(P-2)+N-2 is found to decrease as E(c.m.) is decreased. The N+ signal observed in the O+(S-4)+N-2 reaction is attributed to the formation of N++N+O. The pathway of O++N-2-->N++NO to generate Nt is strongly suggested as the major channel in the reactions of O+(D-2,P-2)+N-2, as evidenced by the observation of N+ well below the thermochemical thresholds of O+(D-2,P-2)+N-2-->N++N+O.