Poly(vinyl alcohol) (PVA) nanocomposites containing three different nanofillers are prepared and compared in terms of their thermal properties, morphologies, and oxygen permeabilities. Specifically, pristine saponite (SPT) clay, hydrophilic organically modified bentonite (OMB), and hexadecylamine-functionalized graphene sheets (HDA-GSs) are utilized as nanofillers to fabricate PVA nanocomposite films. The hybrid films are fabricated from blended solutions of PVA and the three different nanofillers. The content of each filler with respect to PVA is varied from 0 to 10 wt%, and the changes in the properties of the PVA matrices as a function of the filler content are discussed. With respect to the hybrid containing 5 wt% of SPT, OMB, and HDA-GS, each layer in the polymer matrix consists of well-dispersed individual nanofiller layers. However, the fillers are mainly aggregated in the polymer matrix in a manner similar to the case for the hybrid material containing 10 wt% of fillers. In the thermal properties, SPT and OMB are most effective when the filler corresponds to 5 wt% and 7 wt% for HDA-GS, respectively, and the gas barrier is most effective with respect to 5 wt% content in all fillers. Among the three types of nanofillers that are investigated, OMB exhibits optimal results in terms of thermal stability and the gas barrier effect.