For an epoxy/carbon fiber/nanoclay/nanosilica quadratic hybrid nanocomposite, the effect of three independent parameters, such as carbon fiber orientation, weight percentage of nanoclay and weight percentage of nanosilica (SiO2), on the nanocomposite tensile and flexural properties was evaluated. The Taguchi orthogonal array design was selected for designing the experiments and 16 specimens were prepared and tested based on designed levels for each response. It was revealed that all input variables have a reverse effect on the corresponding responses and, according to 2D contour plots, the two component interactions (fiber orientation, nanoclay) and (fiber orientation, nanosilica) are significant for both tensile and flexural strength properties, whereas the other interaction between nanosilica and nanoclay has no pronounced effect on any of the desired responses. Stress-strain plots show that hybrid nanocomposites with different fiber orientations exhibit higher tensile and flexural strength values, higher elongations at rupture, but lower elastic moduli, as compared to epoxy-nanosilica, epoxy-nanoclay and pure epoxy ones.