This study provides fundamental information about the influence of salt on the physicochemical stability of oregano essential oil (EO) and its main components incorporated in a nanoemulsion delivery system containing Tween 80 (T80) emulsifier. The emulsion stability was found to be strongly correlated with the lipid phase composition and the type of salts. The oregano essential oil nanoemulsions remained stable for several weeks in the absence of salts. Moreover, they were insensitive to tetrabutylammonium bromide, whereas similar to carvacrol emulsions, they exhibited a rapid phase separation and oiling-off in the presence of sodium chloride. On the other hand, high oleic sunflower oil (HOSO) and p-cymene emulsions remained stable in the presence of NaCl. Addition of 70 and 80% HOSO to the lipid phase of oregano EO and carvacrol, respectively, was found to be sufficient for the formation of emulsions with a high stability to 1.7 M NaCl. Hereby, the morphology of the oregano EO emulsions after 30 days of storage in the presence of NaCl was visualized using a transmission electron microscope. The determination of the surface load and area per surfactant molecule by interfacial tension (IFT) measurements and quartz crystal microbalance with dissipation revealed the dehydration of the polyoxyethylene groups of T80 in the presence of salt. The thickness of the T80 adsorbed layer onto solid hydrophobic and hydrophilic surfaces was significantly lower (p < 0.05) in the presence of sodium chloride. It is hypothesized that a combination of Ostwald ripening and coalescence due to an IFT increase and dehydration was responsible for the instability of the emulsions containing the more polar oregano EO and carvacrol in the presence of salt. The results obtained in this study could be useful for the formulation of essential oil nanoemulsions in the presence of salts applicable in food, pharmaceutical, and personal care products.