Your first question may well be, "What the *$#%! is a Feghoot?" So here is what little I know about the origins of the word, which is probably more than should be known and is certainly more than any healthy mind should know. Punch-lines in this discussion are linked to stories below that lead to them. Proceed at your own risk. Remember from this point on, you asked for it and you have only yourself to blame. You can't claim you weren't given fair warning.
A Feghoot is particularly bad play on words. They are best (?) if the sounds of the words are reversed and not just rhymed; like a spoonerism which transposes initial sounds of words. (Thus the punch-line "People who live in grass houses should not stow thrones"1 is better than "He finally got his heart's desire—seeing linoleum blown apart."2. (A Feghoot may have a spoonerism but a spoonerism alone does not a Feghoot make.)
Second best (?) are those which use near homonyms of words in the original adage to provide the punch-line of an improbable story. (Thus, "Pardon me, Roy, is that the cat that chewed your new shoes?"3) Feghoots are closely related to shaggy dog stories, the difference being that shaggy dog stories do not include the play on words, and so really are boring. My voluminous reference library and dictionary collection does not include "Feghoot" (probably to discourage their spread and contamination of the body politic) and my encyclopedic mind recalls only that in the dark and muddy history of Feghootia there was a character named Ferdinand Feghoot (perhaps fictional) whose name became inextricably intertwined with these horrible puns, perhaps in that same way the ethnic jokes about the Irish came to be known as Pat and Mike stories.
Having been relentlessly pursued by a reference librarian (who, for her own protection, shall remain anonymous), I did some further research and found the following references in publications of the Mensa Isolated Mensan Special Interest Group which is an organization of people who have nothing better to do than engage in such perversions of thought.
"The official IM definition ... is: A shaggy dog story with a spoonerism punchline (in the best of all possible worlds—the actual item rarely measures up to the definition.)" Isolated M (Mensa Ltd., Nov 1996, p. 6)
"We, members of the IM SIG, stand as the last bastion against the extinction of that most Novel art form ..., the Feghoot. David Koblick, present in the delivery room at the birth of the Feghoot, urges us to write on, especially with a science fiction theme, befitting the Feghoot's roots in Fantasy and Science Fiction Magazine, which alas has turned its back on the poor orphaned Ferdinand Feghhoot and no longer publishes stories of his adventures. The LGR has taken sweet Ferdinand into its warm and loving home, and it is up to us to nuture Ferdie to full and robust health." Isolated M (Mensa Ltd., Dec 1996, p. 18) [LGR is an abbreviation of Little Green Rag, a term of endearment for the publication which refers to its always green-paper cover.]
"...Grendel Briarton, the inventor of Feghoots, whose proper name is Reginald Bretnor, ... is a resident of Milford, Oregon. He is the author of two books on Feghoots, Through Time and Space With Ferdinand Feghoot, and The Complete Feghoot, both available in paperback. Mr. Briarton has kindly permitted the use of the word Feghoot. Feghoots are properly science-fiction shaggy dog stories with a spoonerism last line ...." Fowley, Harper, Feghootia (GRF Defense Fund, no address, 1979, p. iii) [Can you imagine entire books of these? Horrifying isn't it?]
"David Koblick has all the credentials needed to teach the origin of Feghoots. David writes that in the early 1950s, Tony Boucher and J. Francis McComas co-edited (always a questionable arrangement at best) The Magazine of Fantasy and Science Fiction. David was a passing acquaintance of J. Francis, but he knew Tony quite well; thus he had a contemporary interest in their magazine. One of magazine's writers was Reginald Bretnor (a.k.a. Grendel Briarton), who told tales of one Ferdinand Feghoot. This original Feghoot was a space adventurer, roaming the galaxy saving himself and others from one danger after another peril. Each event '...ended with a pun that summed up the situation just resolved.' In one well known - possibly the first - adventure, Ferd dealt with another spacer named Stein, who himself escaped by slipping into a time warp. David reports that the particulars are somewhat hazy, but the first Feghoot was probably 'A niche in time saves Stein.'4 Now you have it." Isolated M (October, 1997, page 18).
Note that this story is also credited to Isaac Asimov and comes in a variety of versions, so it may well not be the original Feghoot. It will, however, serve the purpose.
If your perverted brain actually appreciated some of these, here are some links to a couple of collections of shaggy dog stories and Feghoots provided in a desperate effort to save you and discourage perpetuation of these disgusting tales:
Tarzan's tripes forever, and other feghoots
GCFL Archive Punny Week