Optimizing the operating factors in edible oil extraction requires a statistical technique such as a response surface methodology for evaluating their effects on the responses. The examined input factors in this study were the diameter of pressing vessel, VD (60, 80, and 100 mm), temperature, TPR (40, 60, and 80 °C), and heating time, HTM (30, 60 and 90 min). The combination of these factors generated 17 experimental runs where the mass of oil, oil yield, oil extraction efficiency, and deformation energy were calculated. Based on the response surface regression analysis, the combination of the optimized factors was VD: 100 (+1) mm; TPR: 80 °C (+1) and HTM: 60 (0) min); VD: 60 (−1) mm; TPR: 80 °C (+1) and HTM: 75 (+0.5) min and VD: 100 (+1) mm; TPR: 80 °C (+1) and HTM: 90 (+1). The absorbance and transmittance values significantly (p < 0.05) correlated with the wavelength and temperature, but they did not correlate significantly (p > 0.05) with heating time. The peroxide value did not correlate significantly with temperature, however, it correlated significantly with heating time. Neither the acid value nor the free fatty acid value correlated with both temperature and heating time. The findings of the present study are part of our continuing research on oilseeds’ processing optimization parameters.