An experimental and theoretical study is presented on the (4s) 2SIGMA(g)+, (3p) 2SIGMA(u)+, 2PI(u), and (3d) 2SIGMA(g)+, 2PI(g), 2DELTA(g) Rydberg states in O2+. Their spectroscopic properties (T0, omega(e), omega(e) x(e)) have been determined using translational spectroscopy. The Rydberg molecules are formed in collisions of fast O2(2)+ ions with atomic Cs, K, and Na. The potential energy curves of the Rydberg states have been calculated using a self-consistent field/averaged coupled pair functional (SCF/ACPF) method and agree well with the experimental results. The (3p) 2SIGMA(u)+ state is strongly perturbed by the lowest valence state of the same symmetry. The Rydberg-valence interactions leading to the predissociative decay are discussed.