The subtle interplay of noncovalent interaction in enhancing the compatibility between the graphene-based material and the oligomers of polyvinyl alcohol (PVA) and polyacrylamide (PAM) in the solvent phase is unraveled within the framework of all-atom classical force field-based molecular dynamics (MD) simulations. The decomposition of binding free energy analysis demonstrates that the interaction between polymer segments and graphene (G)-surface crucially emanates from the van der Waals (vdW) interactions, while the adsorption of polymer chains on the graphene oxide (GO)-surface is influenced by vdW and electrostatic interactions. The influence of diverse factors including the strain rate, the size of the nanofiller, the number of oligomers, and the thermal quenching rate on controlling the morphology, mechanical, and thermophysical properties of the graphene-reinforced polymer nanocomposites are further explored. The uniaxial deformation simulations of the graphene-reinforced PVA and PAM matrices show that the interfacial mechanical strength is escalated for the G-PVA nanocomposite. The inclusion of graphene nanofiller reduces the polymer chain mobility and increases the intermolecular interaction, which in turn enhances the toughness of the graphene-polymer composites. Increasing the strain rate raises the yield strength and modulus, making the composites appear stronger and stiffer. As evidenced by the predicted glass transition temperature, the thermal stability of the PVA and PAM matrices is significantly improved by the graphene reinforcement.