how does the immediate constituent analysis of the phrase/sentence 聊斋志异 look like? What is the grammatical analysis of this phrase?
What are the parts of speech?
How can the whole sentence be split into smaller logical units?
Is the title itself a real phrase or real sentence?
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.