Hydrogen is a promising green fuel carrier that can replace fossil fuels; however, its storage is still a challenge. Carbon-based materials with metal catalysts have recently been the focus of research for solid-state hydrogen storage due to their efficacy and low cost. Here, we report on the exfoliation of expanded graphite (EG) through high shear mixing and probe tip sonication methods to form graphene-based nanomaterial ShEG and sEG, respectively. The exfoliation processes were optimized based on electrochemical capacitance measurements. The exfoliated EG was further functionalized with palladium nanoparticles (Pd-NP) for solid-state hydrogen storage. The prepared graphene-based nanomaterials (ShEG and sEG) and the nanocomposites (Pd-ShEG and Pd-sEG) were characterized with various traditional techniques (e.g., SEM, TEM, EDX, XPS, Raman, XRD) and the advanced high-resolution pair distribution function (HRPDF) analysis. Electrochemical hydrogen uptake and release (QH) were measured, showing that the sEG decorated with Pd-NP (Pd-sEG, 31.05 mC cm−2) and ShEG with Pd-NP (Pd-ShEG, 24.54 mC cm−2) had a notable improvement over Pd-NP (9.87 mC cm−2) and the composite of Pd-EG (14.7 mC cm−2). QH showed a strong linear relationship with an effective surface area to volume ratio, indicating nanoparticle size as a determining factor for hydrogen uptake and release. This work is a promising step toward the design of the high-performance solid-state hydrogen storage devices through mechanical exfoliation of the substrate EG to control nanoparticle size and dispersion.