Refractory high-entropy or medium-entropy alloys (RHEAs, RMEAs) exhibit outstanding strength and hold significant promise for high-temperature applications. However, their pronounced brittleness at room temperature restricts their industrial application. Recently, the introduction of interstitial oxygen has proven effective in refining the microstructure and improving the mechanical properties of RMEAs. In this study, we investigated the effect of interstitial oxygen content ranging from 0.5 to 6 at.% on the microstructures and mechanical properties of TiZrNb MEA. The alloys display a single BCC structure, showing a dendritic crystal morphology. At an oxygen content of 4 at.%, the alloy shows a room-temperature compressive yield strength of 1300 MPa and compressive strain of over 50%, achieving a balanced strength and ductility combination. Moreover, it shows excellent high-temperature mechanical properties, with yield strength exceeding 500 MPa at 800 °C. The Toda-Caraballo and Labusch theoretical models were used in the study to clarify the strengthening mechanism of the alloys, and the theoretical yield strengths obtained by calculation coincided with the experimental yield strengths. This validation not only confirms that the primary strengthening mechanism is solid solution strengthening, but also proves the reliability of the model in predicting the mechanical properties of MEAs and provides a theoretical basis for the use of interstitial atoms to strengthen MEAs.