By solving the three-dimensional Schrödinger equation with a second-order implicit Finite Difference Method (FDM), the combined effects of temperature, morphology, hydrostatic pressure, and transverse electric field on the nonlinear optical rectification (NOR) of GaAs/Al_εGa_1−εAs elliptical quantum rings are examined. The NOR amplitude is twelve times enhanced and a noticeable blue shift is induced in the THz region when the electric field is increased. Consequently, with the electric field of 1 × 10⁵ V/m, the NOR magnitude achieves its maximum value of 17.116 × 10⁵ m/V. Additionally, when the electric field is aligned along one side of the system’s in-plane cross-section, the strongest amplification takes place. However, with corresponding spectrum shifts, the NOR intensity rises with temperature and falls with hydrostatic pressure. Additionally, changing the transverse profile of the quantum ring from triangular to parabolic broadens the carrier wave functions and has a considerable impact on the NOR coefficient. These findings provide important information for the construction of high-performance, tunable THz optoelectronic devices by demonstrating effective external and structural tuning of NOR.