The application of graphene nanoplatelets (GNPs) in polymer composites is a challenge due to their high tendency to agglomerate and restack during processing. In this work, alkyl phosphonium-based ionic liquid was used to assist the dispersion of GNP in an ethylene-vinyl acetate (EVA) matrix, through a melt-mixing procedure. The mechanical properties and creep resistance of the films prepared by the film extrusion process were evaluated. The results demonstrated that the noncovalent treatment of GNP with the ionic liquid (IL) enhanced the electrical conductivity and creep stability of the EVA composites. The microwave absorbing properties were studied in the X-band and Ku-band. A reflection loss (RL) of −15 dB for EVA containing 0.5 wt% of GNP and 1:1 wt% of GNP/IL was achieved. The use of a multi-layered structure containing thin film layers was efficient for enhancing the microwave absorbing performance, with a minimum RL of −24.6 dB and effective absorption bandwidth of 4.3 GHz. This result is attributed to the internal reflection and scattering of the radiation between layers. The use of simple, low-cost materials and procedures, combined with the system’s excellent mechanical and electrical properties, makes it a promising candidate for multifunctional applications as electrostatic dissipative and microwave absorbing materials for electronic packaging and other electronic devices.