We might say he's making fun of writers who view books as objects that can only be read. By parodying the idea that books can serve one limited purpose, he demonstrates that books can be so much more. He shows us you can cut parts out of books, read books out loud, record what you're reading, and even put on a live reenactment. Again, we might say Barth uses parody to show us how books can lend themselves to multiple mediums.

Barth might also be using parody to make fun of other famous writers. In "Night-Sea Journey," the sperm writes, "I have seen the best swimmers in my generation go under." What does this line remind you of? If you've read Allen Ginsberg's famous poem Howl, then you might know that it starts off with, "I saw the best minds of my generation destroyed by madness."

Perhaps Barth is using parody to help us think of other writers. Maybe he's parodying them to show us that, even if these other writers have had a serious cultural impact, it's still ok to make fun of them: it's not like they're gods.

One last thing: you might want to look at "Petition" and see how the brother's letter pokes fun at the use of letters in novels. Think about some of the classic novels you've read. Is there not typically a part where the author includes a letter from one character to another? You might want to think about how Barth calls attention to how contrived and tedious those letters can sometimes be.

Barth's story is crammed with metafictional devices from the first paragraph on. These devices are a kind of running commentary on his writing technique and on the technique of others. In the midst of his narrative, he breaks into declarations about the standard ways of doing things in fiction, such as telling us how italics are used, but also telling us that in manuscript (at the time of his writing, when authors still had to use typewriters instead of computers!) this is accomplished through underlining. Barth talks about the method by which writers introduce characters and describe them to the reader. The impression is that he's teaching a literature class, but not necessarily one in which the students are sophisticated enough to know the basic elements of writing. He quotes a popular song of the 1940's and has the need to tell us it's a popular song (something most "conventional" fiction writers leave us to figure out on our own) and also telling us didactically that it is feminine-rhymed. He mentions Joyce's Ulysses and has the need to explain in simple terms the unique qualities of it.

This last point is especially interesting. If the principle of metafiction is to provide an internal commentary on the writing—in effect destroying the conventional illusion of a fictional narrative as of something that really took place—Barth does so in a deliberately obvious or even unsubtle manner. This does suggest parody, a parody of the self-consciousness and the avant-garde nature of modernism. Barth also parodies some elements of pre-twentieth century fiction. It was typical of authors before 1900 to be deliberately unspecific about dates and place names, for instance. Barth mimics this convention, saying his story takes place in the year "19—". In this case, like those modernist composers who, in their music, recreate or quote Romantic music from long ago, Barth creates a cumulative type of fiction that seems to straddle both modernism—creating his own type of post-modern fiction—and the traditional narrative fiction of his time and ours, which has survived the onslaught of change.

As you know, postmodernism sees "art" in very open, flexible, and fluid terms: it is very self-conscious (metafiction), a mix of several styles and media, even if means art as a blatant rip-off of another work (parody).  Most notably there is an element of globalization and mass (mass media, mass communication, mass consumption, etc...).

Lost in the Funhouse, like other metafiction short story collections like The Things They Carried, uses embedded narrators, frame stories, shifts in chronology, and multiple personas.  Barth has admitted that his style is meant to...

‘‘shaking up bourgeois notions of linearity and connectivity and ordinary, realistic description of character, ordinary psychological cause and effect.’’

in order to...

‘‘begin with the assumption that art is an artifice, that it has an element of artifice in it. And so far as wanting our reader to forget that they are reading a novel, we are more inclined . . . to remind them from time to time that this is a story, not that this is only a story, but whatever else it is, it is a story. You’re enthralled, you’re spellbound, if we are doing our work right, by a storyteller, and do not confuse this with reality. Art ain’t life.’’

So, Barth uses a nesting of stories, each parodying the others, even parodying mythological stories (like Proteus), all in an attempt to break down the fourth wall between the speaker and audience.  His recursive style echoes all other stories as it echoes its own and, therefore, becomes connected by its own disconnectedness.

In the Author's Note, John Barth tells us that Life in the Funhouse is "neither a collection nor a selection" of short fiction. Rather, it's a “series” of “items.” Indeed, part of the fun or humor of Barth's book is that we don't know what we're getting ourselves into from one item to the next. Maybe we’ll have something like a typical story. Maybe, as with the first item, we’ll just have to cut something out. We could say Barth uses humor to show us the different things we can do with—and to—one book.

The stories that more or less meet our definition of a typical story tend to use humor to make fun of other, more serious literary genres and devices. We might say "Night-Sea Journey" lampoons adventure stories as well as characters who are inclined toward long, philosophical monologues.

Barth might also be using humor to get us thinking about more serious issues. In "Petition," we might wonder what the conjoined twin's difficulties tells us about the suffering of "the other." We might also ponder what it tells us about the cruelty of humans, when even someone who is physically joined to another person can still treat that other person like a second-class citizen.