EPR line shape simulations of CH3/SiO2 clathrates and comparison to CH3/N2O and CH3/SiO2 experiments reveal the motional conditions of the CH3 radical up to the unusual regime of its stability, the high-temperature diffusional regime, at 300 K. In the low-temperature region, the CH3 in clathrates is found to rotate around the in-plane axes even at as low temperatures as 3.8 K. However, nonrotating methyls performing only libration about the C-2-axes as well as around the C-3-axis are also found, proving the existence of special sites in the clathrate voids that begin to accumulate a significant fraction of methyl radicals at temperatures below approximately 7 K. A distinctive feature in the spectrum anisotropy and line width temperature profiles is found nearby 25 K, which is interpreted as the radical physisorption inside the voids that occurs with the sample temperature lowering. The unusual increase of the CH3/SiO2 clathrate EPR spectral width with temperature over approximately 120 K has its origin in repeated angular momentum vector alterations due to frequent collisions with the clathrate void walls between periodical free rotation periods. This relaxation mechanism resembles to spin-rotation interaction known only for small molecular species in nonviscous fluids but unknown earlier for methyl hosted in solids.