In this article, a comparative study of biaxial stretching at different stretching ratios for melt mixed high-density polyethylene (HDPE)/carbon nanofiller composites containing 4 wt% multiwalled carbon nanotubes (MWCNTs), graphene nanoplatelets (GNPs) or carbon black (CB) was conducted in order to investigate the influence of the carbon nanofillers on the processability of the material and on its final properties after processing. It is shown that the addition of carbon nanofillers results in a significant strain hardening behavior upon biaxial stretching, greatly improving the deformation stability and thus processability of the material. The reinforcement effectiveness of the nanofillers in strain hardening behavior is CB < MWCNTs < GNPs. The GNPs exhibit the most efficient reinforcement in modulus for the stretched samples, while the CB exhibits the most efficient reinforcement in tensile strength. Biaxial deformation destroys the conductive pathways of the nanofillers due to an increased interparticle distance and the destruction of nanofiller network structure. The MWCNT-filled composites exhibit a more robust conductive network during stretching as a result of more interlacing or entanglement of the one-dimensional nanotubes. The oxygen permeability coefficient of the material decreases significantly with the addition of GNPs, and which can be further reduced by two orders of magnitude after biaxial deformation due to the parallel alignment of two-dimensional GNPs in the stretching plane. This study provides important information on the selection of carbon nanofillers for the processing and design of multifunctional polymer composites.