The purpose of this paper is to connect two critical aspects of nanocomposite materials engineering: the knowledge of the orientational distribution of quiescent or flowing anisotropic macromolecules, and homogenization theory of composites with spheroidal inclusions at low volume fractions. The nano-elements considered herein are derived from the class of high-aspect-ratio nematic polymers, either rod-like or platelet spheroids. By combining the two features, we derive the effective electrical conductivity tensor in closed form. Scaling properties of enhanced conductivity versus volume fraction and weak shear rate become explicit. The most dramatic effect is that the effective conductivity tensor inherits hysteresis, bi-stability, and discontinuous jumps from the isotropic-nematic first-order phase transition. These formulas reveal finer estimates that depend on a competition between two inherently extreme parameters in nematic polymer nanocomposites: the molecular aspect ratio and the conductivity ratio of the inclusions and matrix. Herein, we confine our attention to steady monodomain orientational distributions at rest and in weak shear flows, which serve as benchmarks and guides for future extensions and numerical approaches.