Nanocomposites of epoxidized natural rubber (ENR) filled with graphite (GP), carbon nanotubes (CNTs), and CNTs/GP hybrid fillers were prepared and characterized. It was found that both the gum and filled ENR compounds exhibit a reversion curve, attributed to the breaking of weak -O-O- linkages. Furthermore, increasing GP loadings in ENR-GP and ENR-CNTs/GP hybrid composites lead to elevated cure curves and torque differences, indicating higher crosslink density and stiffness of the vulcanizates. These changes are attributed to the increasing chemical interaction between polar functional groups in ENR molecules and nanofiller surfaces, as confirmed by FTIR analysis. That is, a decrease in OH and epoxide groups, along with an increase in ether linkages were observed. Moreover, ENR-CNTs/GP hybrid composites exhibit even higher curing curves, torque differences, Payne effect, total bound rubber content, electrical conductivity, and dielectric constant due to finer filler dispersion and distribution. This is attributed to the formation of interconnected infinite networks that rapidly reach the percolation threshold concentration. Additionally, the formation of CNTs-GP-CNTs connections enhances mechanical strength, heat conduction, and the tunneling effect of electrons. This confirms the synergistic effects of graphite and carbon nanotube hybrid fillers on key properties in ENR-CNTs/GP hybrid nanocomposites, indicating their potential applications in various fields.