The electrical and mechanical properties of carbon nanotube/polymer nanocomposites depend strongly upon several factors such as CNT volume fraction, CNT alignment, CNT dispersion and CNT waviness among others. This work focuses on obtaining estimates and distribution for the effective electrical conductivity, elastic constants and piezoresistive properties as a function of these factors using a stochastic approach with numerous CNT/polymer realizations coupled with parallel computation. Additionally, electrical percolation volume fraction and percolation transitional behavior is also studied. The effective estimates and percolation values were found to be in good agreement with experimental works in the literature. It was found that with increasing CNT volume fraction, the mechanical properties improved. However, due to the interaction of CNTs with one another through electrical tunneling, the conductivity and piezoresistivity properties evolved in a more complex manner. While the degree of alignment played a strong role in the effective properties making them anisotropic, the effect of waviness was found to be insubstantial.