Is it permissible for a woman divorced from an alcoholic husband to make him relinquish some of his property to her while he is under the influence of alcohol, on the pretext that she has been wronged, and what are the consequences of such an action?

A drunk person's relinquishment of their property is not valid. So, if the one divorcing you relinquishes any of his property to you while he is drunk, that has no اعتبار (legal standing). However, if you have a confirmed right that he denied you, and you could not obtain it except through that stratagem, then that might fall under the issue of al-Zafar (obtaining one's right by force or stratagem) with its conditions.