Interstitial defects are inevitably present in doped semiconductors that enable modern-day electronic, optoelectronic or thermoelectric technologies. Understanding of stability of interstitials and their bonding mechanisms in the silicon lattice was accomplished only recently with the advent of first-principles modeling techniques, supported by powerful experimental methods. However, much less attention has been paid to the effect of different naturally occurring interstitials on the thermal and electrical properties of silicon. In this work, we present a systematic study of the variability of heat and charge transport properties of bulk silicon, in the presence of randomly distributed interstitial defects (Si, Ge, C and Li). We find through atomistic lattice dynamics and molecular dynamics modeling studies that, interstitial defects scatter heat-carrying phonons to suppress thermal transport-1.56% of randomly distributed Ge and Li interstitials reduce the thermal conductivity of silicon by $\sim$ 30 and 34 times, respectively. Using first principles density functional theory and semi-classical Boltzmann transport theory, we compute electronic transport coefficients of bulk Si with 1.56% Ge, C, Si and Li interstitials, in hexagonal, tetrahedral, split-interstitial and bond-centered sites. We demonstrate that hexagonal-Si and hexagonal-Ge interstitials minimally impact charge transport. To complete the study, we predict the thermoelectric property of an experimentally realizable bulk Si sample that contains Ge interstitials in different symmetry sites. Our research establishes a direct relationship between the variability of structures dictated by fabrication processes and heat and charge transport properties of silicon. The relationship provides guidance to accurately estimate performance of Si-based materials for various technological applications.