The use of the appropriate emulsifier is essential for forming a stable nanoemulsion delivery system that can maintain the sustained release of its contents. Health concerns have prompted the search for natural biopolymers to replace traditional synthetic substances as emulsifiers. In this study, an oregano essential oil (OEO) nanoemulsion-embedding system was created using soybean protein isolate (SPI), tea saponin (TS), and soy lecithin (SL) as natural emulsifiers and then compared to a system created using a synthetic emulsifier (Tween 80). The results showed that 4% Tween 80, 1% SPI, 2% TS, and 4% SL were the optimal conditions. Subsequently, the influence of emulsifier type on nanoemulsion stability was evaluated. The results revealed that among all the nanoemulsions, the TS nanoemulsion exhibited excellent centrifugal stability, storage stability, and oxidative stability and maintained high stability and encapsulation efficiency, even under relatively extreme environmental conditions. The good stability of the TS nanoemulsion may be due to the strong electrostatic repulsion generated by TS molecules, which contain hydroxyl groups, sapogenins, and saccharides in their structures. Overall, the natural emulsifiers used in our study can form homogeneous nanoemulsions, but their effectiveness and stability differ considerably.