The importance of vibrational-to-electronic (V-E) energy transfer mediated by spin-orbit coupling in the collisional removal of O₂(X ³Sigma_g^-,upsilo>=26) by O₂ has been reported in a recent communication [F. Dayou, J. Campos-Martínez, M. I. Hernández, and R. Hernández-Lamoneda, J. Chem. Phys. 120, 10355 (2004)]. The present work provides details on the electronic properties of the dimer (O₂)₂ relevant to the self-relaxation of O₂(X ³Sigma_g^-,upsilo>>0) where V-E energy transfer involving the O₂(a ¹Delta_g) and O₂(b ¹Sigma_g⁺) states is incorporated. Two-dimensional electronic structure calculations based on highly correlated ab initio methods have been carried out for the potential-energy and spin-orbit coupling surfaces associated with the ground singlet and two low-lying excited triplet states of the dimer dissociating into O₂(X ³Sigma_g^-)+O₂(X ³Sigma_g^-), O₂(a ¹Delta_g)+O₂(X ³Sigma_g^-), and O₂(b ¹Sigma_g⁺)+O₂(X ³Sigma_g^-). The resulting interaction potentials for the two excited triplet states display very similar features along the intermolecular separation, whereas differences arise with the ground singlet state for which the spin-exchange interaction produces a shorter equilibrium distance and higher binding energy. The vibrational dependence is qualitatively similar for the three studied interaction potentials. The spin-orbit coupling between the ground and second excited states is already nonzero in the O₂+O₂ dissociation limit and keeps its asymptotic value up to relatively short intermolecular separations, where the coupling increases for intramolecular distances close to the equilibrium of the isolated diatom. On the other hand, state mixing between the two excited triplet states leads to a noticeable collision-induced spin-orbit coupling between the ground and first excited states. The results are discussed in terms of specific features of the dimer electronic structure (including a simple four-electron model) and compared with existing theoretical and experimental data. This work gives theoretical insight into the origin of electronic energy-transfer mechanisms in O₂+O₂ collisions.