Sorption and diffusion of binary mixtures of small molecules in model polymer networks is studied via computer simulation. Three types of molecules identical in volume but different in shape and flexibility (compact, linear stiff, and linear flexible) are combined into binary mixtures (compact/linear stiff) and (linear stiff/linear flexible). The relative effects of shape and flexibility on separation factor and diffusion coefficient inside random polymer networks are studied using a molecular dynamics/Gibbs-ensemble Monte Carlo hybrid technique. In addition the effects of temperature, pressure, and network strand length are considered. We find that the compact molecules are preferentially absorbed into the network at all strand lengths and temperatures considered here. Flexibility only leads to minor preferential sorption under most conditions. Diffusion coefficients of the competing species inside the network are found to agree within the error bars.