Existing experimental (2+1) REMPI spectra for transitions into rotationally resolved levels of the 3s sigma(g) d (1)Pi(g) and 3s sigma(g) C (3)Pi(g) Rydberg states of O-2 have been rotationally analyzed, resulting in the first characterization of rotational perturbations in d(v=1-3) and C(v=2). In addition, the results of this analysis have been interpreted with the aid of a coupled-channel Schrodinger-equation (CSE) model of the interacting electronic states. The identification and characterization of perturbations in the d and C states have allowed the nature of the interactions between the 3s sigma(g) (1,3)Pi(g) Rydberg states and the parallel to (1)Pi(g) valence state to be clarified and a realistic empirical potential-energy curve for the parallel to (1)Pi(g) state to be determined. While it is found that first- and second-order interactions with the parallel to (1)Pi(g) valence state are responsible for the strongest perturbations observed in d(v=1-3) and C(v=2), additional weak perturbations found in d(v=2 and 3) are shown to result from a second-order interaction with the parallel to (1)Delta(g) valence state. These weak perturbations, including an extra level observed for d(v=3, J=17), appear to be the first experimental evidence for the parallel to (1)Delta(g) state, long predicted theoretically. Finally, detailed comparisons between experimental spectra and d (1)Pi(g)<--<--a (1)Delta(g)(1,0), (2,0) and (3,0) (2+1) REMPI spectra calculated using the CSE model are presented which support and illustrate these conclusions.