Exploiting polymer nanocomposites as dielectric and heat storage devices is an important approach to develop high performance materials. Graphite (GT), thermally reduced graphene oxide (TRG), and hybrid consisting of TRG and ionic liquid (1-Ethyl-2, 3-dimethylimidazolium bis (trifluoromethylsulfonyl) imide) modified carbon nanotubes (IMCNT) were added to natural rubber and membranes were fabricated via melt mixing method. The amount of the GT, TRG, TRG+IMCNT used in this work was in the range of 0.5 to 5 wt%. Mechanical properties of NR nanocomposites revealed that the hybrid (TRG+IMCNT) (5 wt%) system showed high tensile strength, high modulus and low elongation at break as compared to neat NR, NR reinforced with GT (5 wt%) and NR reinforced with TRG (5 wt%) systems owing to the synergistic hybrid effect caused by the network formation of the hybrid fillers inside NR matrix. Dielectric properties of the prepared membranes were studied at 2.5, 10 and 20 GHz in the microwave frequency region using a Split Post Dielectric Resonator (SPDR) based technique. The incorporation of micro and nanofillers in the natural rubber (NR) matrix results in consistent improvement in dielectric constant and lower loss tangent values. In certain cases the samples containing 5 wt% of filler exhibited high loss or conducting behaviour at higher frequencies (10 and 20 GHz). Different techniques had to be employed for measuring the dielectric constant and loss tangent of the prepared membranes where they showed a high loss or conducting behaviour. Moreover, thermal history like glass transition temperature and the change in heat capacity were estimated using Differential Scanning Calorimetry (DSC). In addition, the dispersion of micro and nanofillers inside the NR was estimated using X-ray followed by Transmission Electron Microscopy for the morphology architecture of nanofillers. The morphology of the prepared membranes was correlated with the mechanical, dielectric and thermal properties. The hybrid system (TRG+IMCNT) exhibited high dielectric constant (5.6) and low heat capacity value (0.32 J/g/°C) as compared to GT and TRG systems.