In previous studies, we provided a novel systematization of alpha-decaying even-even and even-odd nuclei starting with the classically adopted mechanism [T. Yarman et al., Eur. Phys. J. A 52 (2016) 140; Eur. Phys. J. A 53 (2017) 4]. Knowing beforehand the measured decay half-life, we had taken as a parameter the probability of the a-particle as being first born in a unit period of time, within the parent nucleus before it is emitted out. We thence developed a scaffold based on shell properties of families composed of "alike nuclei". Along the same line, we now present a systematization of odd-even (OE) as well as odd-odd (OO) nuclei. We apply our approach further to the investigation of the effect of pairing (e.g., the effect when the number of nucleons is increased by one neutron), and that of unpairing (e.g., the effect when the number of nucleons is decreased by one neutron); thus it becomes an even number for the case of odd-even nuclei (Case OE), and an odd number in the case of odd-odd nuclei (Case OO). For the first case (OE), we pick the exemplar set Re-161, Fr-217, Bk-243, (263)Db; where we delineate by, respectively, Re, Fr, Bk, and Db all of the odd-even or odd-odd isotopes that neighbor the four mentioned odd-even isotopes on the proposed scaffold. We proceed in the same way for the second case (OO). Thus, we choose the exemplar set of odd-odd nuclei Ir-172, Ac-218, Es-244. We then gather all of the Ir, Ac, and Es odd-odd and odd-even isotopes that neighbor the three mentioned odd-odd isotopes on the proposed scaffold. We show that, in the former case, pairing, as expected, generally increases stability of the given nucleus; and in the latter case, unpairing works in just the opposite direction - i.e., it generally increases instability. We disclose "stability peaks" versus Z for both sets of nuclei, we tackle here. Furthermore, we present a study to highlight an outlook of "odd-A nuclei" at hand. Contrary to the general expectation, we unveil no systematic on that.