Interaction potentials of the (3)Pi and (3)Sigma(-) electronic states of the Rg-O(P-3) systems (Rg=He-Kr) are computed at the coupled cluster single, double (triple) level of ab initio theory using extended basis sets augmented by bond functions. The ab initio potentials agree well with the scattering potentials determined from experiments in molecular beams [Aquilanti et al., J. Chem. Phys. 89, 6157 (1988)]. Both sets of the interaction potentials are employed for accurate close-coupling calculations of cross sections and rate constants for intramultiplet transitions in collisions of O(P-3(j)) with Rg atoms and analytical approximations for temperature dependencies of rate constants over temperature interval 50-3500 K are proposed. The sensitivity of the dynamical results to the nature of Rg atoms and interaction potentials is analyzed and the dynamics of intramultiplet mixing in O(P-3(j)) is investigated in both high- and low-energy limits.