Oils derived from non-traditional seeds, such as safflower, milk thistle, and black cumin seeds, have recently grown in popularity. Seed oil is in high demand due to consumer interest in illness prevention and health promotion through healthier diets that include a high concentration of monounsaturated and polyunsaturated fatty acids and antioxidant phenolic components. This study assessed the quality characteristics of cold-pressed seed oil at three unique storage times: at the beginning of the trial (i.e., before storage), after 2 months, and after 4 months. The results of the performed analyses indicate that the acidity of extracted black cumin, safflower, and milk thistle seed oil fluctuates considerably over time. The highest acidity level change was detected for black cumin seed oil, from 10.26% after the extraction to 16.96% after 4 months of storage at 4 °C. Consequently, changes between pre- and post-storage peroxide concentrations were discernible after four months. Peroxide value in milk thistle and safflower seed oils increased by 0.92 meq/kg and 2.00 meq/kg, respectively, during the assessed storage time, while that of black cumin was very high and fluctuated. The storage period substantially affects oxidative changes and the oxidation stability of the oil. Major changes were observed in the polyunsaturated fatty acids in seed oil during storage. The essential changes were detected in the black cumin seed oil odor profile after 4 storage months. Their quality and stability, as well as the nature of the changes that occur during the storage of oil, require extensive investigation.