Can the phrase 不条理劇 "a theatre of absurd" be used figuratively in Japanese? Would it be valid in casual Japanese conversation to use the term {} or {} to describe a situation in which for example two parties A and B are talking to each other using nonsensical arguments or acting in illogical way in response to each other? If not what other word might be used to describe such a situation?

You mean, to describe such nonsensical situations in general, rather than to actually talk about this kind of theatre? Then, no, I think most people do not recognize the word (), and I have never heard or seen "" or something like that.

The first word that came into my mind to describe such a situation is , which is a loanword from "surrealism". I don't know the usage of this word in English, but Japanese people use often (at least more often than or ) to describe something nonsense yet funny, impressive but difficult to interpret. It's too difficult for me to fully convey the feelings of this word, but don't believe the dictionary definition and try googling or .