Clay minerals abound in sedimentary formations and the interaction of reservoir gases with their sub-micron features has direct relevance to many geo-energy applications. The quantification of gas uptake over a broad range of pressures is key towards assessing the significance of these physical interactions on enhancing storage capacity and gas recovery. We report a systematic investigation of the sorption properties of three source clay minerals - Na-rich montmorillonite (SWy-2), illite-smectite mixed layer (ISCz-1), and illite (IMt-2) - using CO and CH up to 30 MPa at 25 to 115 °C. The textural characterization of the clays by gas physisorption indicates that micropores are only partly accessible to N (77 K) and Ar (87 K), while larger uptakes are measured with CO (273 K) in the presence of illite. The supercritical excess sorption experiments confirm these findings, while revealing differences in uptake capacities that originate from the clay-specific pore size distribution. The Lattice Density Functional Theory (LDFT) model describes accurately the measured sorption isotherms by using a distribution of properly weighted slit pores and clay-specific solid-fluid interaction energies, which agree with isosteric heats of adsorption obtained experimentally. The model indicates that the maximum degree of pore occupancy is universal to the three clays and the two gases, and it depends solely on temperature, reaching values near unity at the critical temperature. These observations greatly support the model's predictive capability for estimating gas adsorption on clay-bearing rocks and sediments.