In this work, poly(vinyl alcohol) (PVOH)/graphene (GN) oxide/clay aerogels were prepared using montmorillonite (MMT) and kaolinite (KLT) as fillers. This work paves the way for the development of aerogels filled with MMT or KLT with high conductivity. The mechanical properties of the polymer/clay aerogels are enhanced by incorporating GN into these systems. These composite materials have an enhanced thermal stability, and the combination of PVOH and GN leads to interconnected channels which favored the conductivity when a clay (MMT or KLT) is added to the mixed PVOH/GN matrix. However, after compressing the samples, the conductivities drastically decreased. These results show that the design of solid MMT/GN and KLT/GN composites as aerogels allows maximizing the space utilization of the electrode volume to achieve unhindered ion transport, which seems contrary to the general design principle of electrode materials where a suitable porous structure is desired, such as in our uncompressed samples. These findings also demonstrate the potential of these materials in electrodes, sensors, batteries, pressure-sensing applications, and supercapacitors.