This question concerns both Western and Eastern cultures. For example, would an ancient Greek ever express concern with some sort of "by the power of Zeus!" saying? Are there any writings that demonstrate a similar and commonly used expression in places like China or Japan?
I can speak for Latin: phrases such as 'mehercule'/just 'hercule', relating to Hercules, 'ecastor', to Castor, 'edepol', to Pollux, and 'pro di imortales', which means 'by the immortal gods' were used with this meaning.