Nuclear potential energy surfaces as a function of deformations are calculated on the basis of a modified oscillator model. In particular, quadrupole ( P2) and hexadecapole ( P4) deformations are considered. The average behavior of the surface is normalized to that of a liquid drop through the employment of a generalized Strutinsky prescription. In this way a synthesis of the single-particle model and the liquid-drop model is obtained. Lowest minima in the potential energy surfaces give the ground state masses and distortions. These results compare extremely well with experimental data. Spontaneous fission half-lives are also obtained. The inertial parameters associated with fission barrier penetration are derived empirically as well as by a microscopic model. Shape (fission) isomeric states are also found. Their N and Z dependence in the present model are discussed and results tabulated. The calculations are extended to the predicted superheavy region around Z = 114 and N = 184. The total overall stability with respect to alpha and beta decay, and spontaneous fission is found to be most favorable in the vicinity of Z = 110 and N = 184. Detailed diagrams and tables are exhibited.