The chemical freeze-out parameters in central nucleus-nucleus collisions are extracted consistently from hadron yield data within the quantum van der Waals (QvdW) hadron resonance gas model. The beam energy dependence of both, skewness and kurtosis, of baryonic- and electric charges are predicted. The QvdW interactions in asymmetric matter, Q/B≠0.5, between (anti-)baryons yield a non-congruent liquid-gas phase transition, together with a nuclear critical point (CP) at a critical temperature of $\T_c$=19.5 MeV. The nuclear CP yields the collision energy dependence of the skewness and the kurtosis to both deviate significantly from the ideal hadron resonance gas baseline predictions even far away, in ($T$,$\mu_B$)-plane, from the CP. These predictions can readily be tested by STAR and NA61/SHINE Collaborations at the RHIC BNL and the SPS CERN, respectively, and by HADES at GSI. The results presented here offer a broad opportunity for the search for signals of phase transition in dense hadronic matter at the future NICA and FAIR high intensity facilities.