What is the optimal course of action, Islamically, if a wife is subjected to a malicious gaze or verbal harassment from a man, in the absence of police: Is it permissible to offer advice, or to strike, or to curse?

Protecting what is sacred is a characteristic of a believer. If you see someone harassing your wife with words or actions, you are permitted to denounce him, and this denouncement becomes an obligation, either individually incumbent (fard ayn) or communally incumbent (fard kifayah), and it does not cease merely due to the assumption of its futility. This must be done while observing the manners of enjoining good and forbidding evil. You are not permitted to insult him, as insulting is forbidden except with a legitimate legal justification. As for striking, as a form of changing with the hand, some scholars have permitted it to prevent the occurrence of evil or its persistence, while observing the Sharia-compliant regulations. However, it is not permissible after the evil has occurred, because it is for discipline, and you do not have the authority to discipline him.