The increasing consumption of plastic waste and the depletion of wood resources have made the development of wood–plastic composites based on recycled materials an important area of research. The aim of this study was to investigate the effect of nanoclay on the mechanical and thermal properties of composites fabricated from old corrugated container (OCC) pulp and recycled polystyrene (rPS). The nanocomposites were prepared using a twin-screw extruder followed by injection molding. Their mechanical properties, including tensile strength, tensile modulus, flexural strength, flexural modulus, and impact strength, were evaluated according to ASTM standards. Thermal behavior was assessed using thermogravimetric analysis (TGA). The results showed that increasing the nanoclay content from 0 to 9 wt% reduced the tensile strength, tensile modulus, flexural strength, flexural modulus, and impact strength by approximately 18%, 14.5%, 13%, 18%, and 14%, respectively. In contrast, the incorporation of nanoclay improved the thermal stability of the nanocomposites, as evidenced by an increase in the onset degradation temperature from 228 to 232 °C and an increase in the residual weight at 700 °C from 11.66% to 18.68%. These findings indicate that although nanoclay enhanced the thermal stability of the nanocomposites, it did not improve their mechanical properties under the formulation and processing conditions employed in this study. Therefore, optimization of the nanoclay content, coupling agent concentration, and processing conditions is essential to achieve a balanced improvement in both the mechanical and thermal properties of this type of nanocomposite.