how does the immediate constituent analysis of the phrase/sentence 聊斋志异 look like?
聊斋志异 is the name of an ancient novel, which is a collection of nearly 500 mostly supernatural tales written by Pu Songling in Classical Chinese during the early Qing Dynasty.

Source: Strange Stories from a Chinese Studio

聊 means chat, 斋 means room, and 聊斋 is the name of the author's study room/studio.

志 means record, 异 means strange things, 志异 means to record the strange things, so 聊斋志异 is a stories' collection about strange things recorded by the author at his study studio named 聊斋.

BTW: 聊斋志异 could be shortened as 聊斋.