Clue: Clue is clearly the illicit stepchild of Murder by Death. It is not as tightly written nor as well-acted as its inspiration. For good or for bad, it delivers a far more spoof-y feel, closer to the joyful ridiculousness of Airplane ("Don't call me Shirley") than to straight comedy. Like many films associated with Leslie Nielsen, Airplane utilizes the throw-enough-jokes-on-the-page-hey!-some-will-stick approach. Clue sadly doesn't have Leslie Nielsen but it does have the same hyperactive feel. And some of the jokes do stick! The most memorable scene of Clue is when the characters wander collectively from room to room staring blankly at the accumulating dead bodies.
On the literature front, Agatha Christie spoofed fictional detectives in her Tommy and Tuppence short stories; Partners in Crime uses the conceit that every crime that Tommy and Tuppence solve bears resemblance to the style of crime utilized by a (then) famous mystery author. And yes, Christie even spoofed Poirot's little gray cells!
The problem is that in order to get the joke one has to be familiar with the detectives; unfortunately, due to the passage of time, the only detective Christie adequately spoofs is her own! Nobody remembers the others. Partners in Crime is one of Christie's rarely reprinted anthologies.
It is much easier--and much more reliable--to spoof the motifs of the mystery or whodunit: the locked manor house, the mastermind of multiple disguises, the cobwebbed room, the longwinded revelation, the "butler did it" syndrome. The most basic rule of satire is If the audience doesn't know what you are spoofing, they won't get the joke.
Unless, the writing accounts for audience ignorance.
My favorite example of a mystery spoof that doesn't rely too much on audience knowledge is Frasier's "Ham Radio." Frasier persuades the radio station where he works to put on an old-time radio mystery. Being Frasier, he starts to micromanage everybody. Consequently, when the performance goes live, craziness ensues, including Niles (Frasier's brother) killing off the twelve characters that Frasier is forcing him to voice by "shooting" them (popping balloons). As listener Marty exclaims, "I don't remember these programs being so goofy!"
"Ham Radio" is the perfect spoof because it is funny on different levels. The characters are funny. The regular jokes are funny. The mystery spoof jokes are funny. AND the references to old-time radio programs are funny. A later episode, "Out with Dad" is funny for a similar reason. One doesn't have to know anything about opera to find the pay-offs hilarious, but it is a nice bonus if you do.