In this study, we investigate the piezoresistivity of metal nanowire networks embedded in a polymer, which has been widely used as a highly-stretchable strain sensor, by varying the orientation distribution of nanowires. For simplicity, we assume the affine transform of the nanowire network upon stretching and compute the effective conductivity of the nanowire network by recognizing the percolation network connecting low and high voltage boundaries. Orientation-dependence is then studied firstly by varying the range of polar angle and secondly by changing the degree of alignment along loading direction. Since nanowires are embedded in thin nanowire-polymer film in most stretchable sensor applications, instead of having random orientation distribution over full solid angle, nanowires have a limited range of polar angle distribution around 90° (when the surface normal vector of a thin film is given as the zenith direction). We show that the gauge factor (relative resistance change over applied mechanical strain) decreases as the polar angle distribution gets narrower. We then study the effect of nanowire alignment on the piezoresistive response, by assuming partial alignment distribution along the tensile direction. We find that a wide range of the gauge factor, from negative to positive, appears as the initial partial alignment angle varies, and explained such response by analyzing the relative electrical path change between a pair of nanowires. Our study deepens the understanding on the percolation-network based piezoresistive sensors and provides a guideline for designing a stretchable strain sensor with the desired gauge factor.