Aimed at ionization balance and spectral analysis of UV and X-ray sources, we present self-consistent sets of photoionization cross sections, recombination cross sections, and rate coefficients for photoionization of, and recombination to, Li-like O VI and He-like O VII. Relativistic fine structure is considered through the Breit-Pauli R-matrix (BPRM) method in the close-coupling approximation, implementing the unified treatment for total electron-ion recombination subsuming both radiative and dielectronic recombination processes. Self-consistency is ensured by using an identical wave function expansion for the inverse processes of photoionization and photorecombination. Radiation damping of resonances, important for H-like and He-like core ions, is included. Compared with our previous LS coupling results without radiative decay of low-n (n ≤ 10) resonances, the presents results show significant reduction in O VI recombination rates at high temperatures. In addition to the total rates, level-specific photoionization cross sections and recombination rates are presented for all fine-structure levels n (l SLJ) up to n ≤ 10, to enable accurate computation of recombination-cascade matrices and spectral formation of prominent UV and X-ray lines such as the 1032, 1038 Å doublet of O VI, and the "triplet" forbidden, intercombination, and resonance X-ray lines of O VII at 22.1, 21.8, and 21.6 Å, respectively. Altogether, atomic parameters for 98 levels of O VI and 116 fine-structure levels of O VII are theoretically computed. These data should provide a reasonably complete set of photoionization and recombination rates in collisional or radiative equilibrium.