The solution of the exact integral equation for the liquid pair-structure in the asymptotic strong coupling limit for the plasma, as mapped on the Onsager charge-smearing optimization for the energy lower bound, features “Onsager atoms” and “Onsager molecules”. The universal properties of this asymptotic limit make it a natural reference starting point for an asymptotic strong coupling expansion for the fluid structure and thermodynamics, playing the role of an “ideal liquid” state. In particular, the leading strong coupling terms for the potential energy, direct correlation functions, and screening potentials for the Coulomb and Yukawa mixtures (corresponding to classical plasmas and electron screened classical plasmas), with full thermodynamic consistency, are presented. These are in complete agreement with the Alastuey-Jancovici analysis of early simulations data by Hansen in strong coupling, and with recent highly accurate simulations data of Ogata, Iyetomi, and Ichimaru. Data analysis errors lead Ogata, Iyetomi, and Ichimaru to incorrect results for the short range screening potentials in strong coupling. Their calculations for the short range screening potentials, bridge functions, and enhancement factors for nuclear reaction rates in strongly coupled plasmas, should be revised.