Presently, many researches are directed toward the design of novel superatoms with high nonlinear optical responses. Inspired by a fascinating finding of superatoms which were designed by bonding superhalogen (Al-13 nanocluster) with superalkalis (M3O, M = Na and K), we suggest an effective strategy to form a series of typical donor-acceptor frameworks with high nonlinear optical responses via bonding the superalkalis M3O (Li3O, Na3O, K3O, Li2NaO, Li2KO, Na2LiO, Na2KO, K2LiO, K2NaO, and LiNaKO) with low ionization potential to the superhalogen Al-13 with large electron affinity. The ionization potential, electronic spatial extent, electric field gradient tensors of O-17 nuclei, and natural bond orbital charge values of the superalkalis M3O were also calculated. We found that the M ligands have the remarkable effect on the ionization potential as well as O-17 nuclear quadrupole resonance parameters of the superalkalis M3O. Our results also represented that the bonding superalkalis can efficiently narrow wide HOMO-LUMO gap and considerably enhance first hyperpolarizability of the pristine Al-13, due to electron transfer in this type of superatom. Also, the effect of oriented external electric fields on the nonlinear optical responses of the superatoms M3O-Al-13 has been systematically explored. We found that the first hyperpolarizability of the superatom compounds can be gradually increased by increasing the imposed oriented external electric field from zero to the critical external electric field along the charge transfer direction (M3O -> Al-13). In this respect, this work reveals an effective approach to gradually enhance the nonlinear optical responses of the superatoms through applying oriented external electric fields.