A weak, paradoxically narrow resonance feature (shortly, the r-line) near the O2 fundamental frequency in the collision-induced absorption spectrum of oxygen dissolved in liquid argon and liquid nitrogen (T = 89 K) is resolved for the first time. An accurate band shape fitting routine to separate the r-line from the by-far more intense diffuse background and to study its behavior versus the oxygen mole fraction x which ranged from 0.03 up to 0.23 has been elaborated. At small x (≲0.07), the r-line intensity was found to scale as x(2) leaving no doubt that it is due to the solute-solute (O2-O2) interactions. In line with our results on the pH2-LNe cryosystem [Herrebout, Phys. Rev. Lett. 101, 093001 (2008)], the Lorentzian r-line shape and its extraordinary sharpness (half width at half height ≈ 1 cm(-1)) are indicative of the motional narrowing of the relative solute-solute translational spectrum. As x is further raised, ternary solute-solute interactions impede the r-line growth in the O2-LAr spectrum because of the cancellation effect [J. Van Kranendonk, Physica 23, 825 (1957)]. Theoretical arguments are given that multiple interactions between the solutes should finally destroy the solute-solute induced r-line when the mixed solution approaches the limit of the pure liquid (x = 1). Interestingly, the nonbinary effects are too weak to appreciably affect the quadratic r-line scaling in the O2-LN2 cryosystem which persists up to x = 0.23. It is emphasized that studies of the resonant features in the collision-induced spectra of binary cryosolutions open up unique opportunities to spectroscopically trace the microscopic-scale diffusion.