Employing chemical vapor deposition technique, multi-walled carbon nanotubes (CNTs) were synthesized over different catalysts (Fe, Ni, and Co) spanning a broad range of temperatures, i.e., from 550˚C to 950˚C at 100˚C intervals. Synthesized CNTs were melt-mixed into a poly(vinylidene fluoride) (PVDF) matrix at different concentrations. Characterization of the nanofillers, i.e., thermogravimetric analysis and transmission electron microscopy, and characterization of the nanocomposites, including optical microscopy, transmission electron microscopy and AC conductivity, revealed that synthesis temperature or synthesis catalyst greatly affected physical features of CNTs (e.g., length and diameter) and CNT network formation within the nanocomposites. To get further insight into the nanofillers network structure, viscoelastic behavior of polymer nanocomposites was studied. Accordingly, we carried out linear and nonlinear rheological tests on CNT/PVDF nanocomposites. The results of linear viscoelastic characterizations revealed significant differences between the viscoelastic behaviour of the prepared nanocomposites, and this was in line with the morphological characterization of the nanofillers and nanocomposites. The data obtained from oscillatory amplitude sweep test were used to evaluate the nonlinear viscoelastic responses under large amplitude oscillatory shear (LAOS) flow. Physical interpretations and structure-property relationships were inferred based on intra- and inter-cycle nonlinear parameters and Lissajous-Bowditch plots. These results showed a strong dissipative nonlinearity at intermediate deformations for samples having the worst conductive network, i.e., nanocomposites containing CNTs featuring large diameter.