We report microwave spectroscopy studies of graphene-based polymer-matrix composite materials subject to uniaxial elongation. The samples were prepared via shear mixing under the same thermal processing conditions of amorphous styrene butadiene rubber (SBR) with quartz grains on the order of micrometers in size and/or graphene sheets with thickness 10-20 nm and average lateral size 200 mu m. An important result is the observation of a significant increase (up to 25%) in the effective microwave permittivity of hybridized nanocomposites comprising both quartz and graphene compared to the nanocomposites with quartz only. We suggest that the coating of quartz grains by graphene sheets is the most likely origin of this synergetic effect. In all cases, we also observe that the permittivity spectrum is unaffected by strain up to 8%. By examining the mechanical response, it is shown that the elasticity network of SBR polymer chains is significantly affected in the rubbery state by filling SBR with graphene and quartz particles.