We develop a statistical mechanical theory of charge storage in quasi-single-file ionophilic nanopores with pure room temperature ionic liquid cations and anions of different size. The theory is mapped to an extension of the Ising model exploited earlier for the case of cations and anions of the same size. We calculate the differential capacitance and the stored energy density per unit surface area of the pore. Both show asymmetry in the dependence on electrode potential with respect to the potential of zero charge, related to the difference in the size of the ions, which will be interesting to investigate experimentally. It also approves the increase of charge storage capacity via obstructed charging, which in these systems emerges for charging nanopores with smaller ions.