Is it possible for a person to be possessed by thousands of jinn, and is it permissible for him to use the "barrel" method (filling it with water, placing headphones reciting the Quran, and then entering it naked) to expel the jinn?

The possession of a human by jinn is possible. The method of ruqyah (exorcism) involves reciting over the afflicted person, or the afflicted person reciting over themselves. Listening to the Quran from a recording is beneficial, but it does not substitute for the reciter's direct reading. A man stripping off his clothes and entering a barrel of water is permissible, provided it does not involve any religious prohibitions, such as the suspicion of jinn whispering, the exposure of 'awrah (private parts), or harm from the water.