A musical theater parody of the 1970s hit television series “Little House on the Prairie” sounds like a great idea. With its cast of straight-laced pioneers and its audacious television plot lines (fires, stagecoach crashes, even an anthrax scare), “Little House” seems ripe for the picking. Plus there are all those weird undercurrents: grown men proposing to girls still in pigtails, witches and faith healers coming to town, people being mysteriously blinded and regaining their sight, Frank and Jesse James hiding out in Walnut Grove. And imagine the musical possibilities – say, a big production number about adopted brother Albert battling his morphine addiction.

Alas, these comic possibilities are largely squandered in “Little House on the Parody,” directed by Andy Eninger and now playing at the New York International Fringe Festival. Respectful to a fault, this is a parody with almost no bite. Writers Becky Eldridge and Amy Petersen, who admit to being devotees of the original Laura Ingalls Wilder books, have written an earnest show with earnest songs like “When Bad Things Happen to Good People.” In “Little House” terms, the tone is more that of Laura’s faithful puppy Bandit than the pack of wild dogs that once attacked the farm.

The loving parody may well be a contradiction in terms. At minimum, it’s a tough way to get laughs. Unwilling to go for the jugular, the writers have almost nowhere else to go. “Little House” runs almost entirely on straightforward caricature. It’s mildly amusing to hear the familiar characters speak their trademark lines – Pa (Pat Shay) gets a laugh every time he says “half pint.” But it’s monotonous going: blind Mary jokes, dumb Carrie jokes, drunk Mr. Edwards jokes, pious Ma jokes, spacey Albert jokes. The lone dynamic character (and the funniest one by far) is Eliza Jane Wilder, the prairie schoolteacher. As portrayed by Dori Goldman, Eliza Jane sees herself as a sexual powerhouse waiting to be discovered. In the show’s best number, “A Talent,” she unbuttons her collar and shakes it with the sly confidence of an MTV dancer.

However, the songs are mostly lackluster. Given the paucity of trained singers in the cast, there are a lot of voices straining for notes. The milquetoast lyrics don’t help, either. Among the dozen original songs are tunes about good elocution, Ingalls family values, and God providing. But even when a song takes a promising comic turn (e.g. butchering Laura’s pet pig for Christmas dinner), the writers quickly back off the joke.

It is one of the ironies of “Little House on the Parody” that its characters are actually less funny than their network television counterparts. Onstage, when Laura gets mad at her schoolgirl nemesis Nellie Oleson, she sticks out her tongue and shakes her fists at her. On television, Laura memorably pushed Nellie’s wheelchair up a massive hill and gave her a shove. The television version of “Little House” may have been styled as family entertainment, but it compulsively crossed lines of good taste and judgment. Sadly, the same cannot be said of “Little House on the Parody,” a piece of family entertainment styled as fringe.

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In the “indisputably fringe” category is the festival entry from Chicago’s avant-garde Trapdoor Theater – a revival of Stanislaw I. Witkiewicz’s hallucinatory drama “The Crazy Locomotive.” Witkiewicz, a Polish painter and philosopher, clearly took art and politics seriously: He killed himself to protest the invasion of Poland in 1939. His 1923 play about man and machine is a discomfiting, ugly trip to the edge. As a locomotive hurtles toward an oncoming train with innocent passengers in tow, the criminally insane Siegfried Tenser (Carl Wisniewski) and his maniacal underling, Nicholas Slobok (John Gray), stoke the fires and brag about being “adrift from all mankind.” Both men are in love with the same woman, Slobok’s fiancee Julia (Nicole Wiesner). The wanton Julia gets off on the idea of imminent death. Writhing in hysterical anticipation, she luxuriates in the caresses of both lovers. “This it the only time in our lives,” she raves, “when we can really gorge ourselves on reality.”

Made up in whiteface, with clown eyes and mouths painted on, the actors seem chillingly inhuman: ruthless junkies looking for their next high. The characters’ remorseless eyes and brittle laughs work as an abrasive, gradually wearing down the audience’s resistance. Likewise, when innocents manage to breach the engine room and beg the sociopaths to stop the train, they’re corrupted in no time.

Witkiewicz’s dark vision of a world where people live by their nerves, seesawing from one high to the next, presses in on all sides. Actors storm the aisles, shout from balconies, stride toward us on film, and take seats in the crowd, uncomfortably close. The play wants to take the whole audience on a bender, and under Beata Pilch’s capable direction, it largely succeeds. “The Crazy Locomotive” is the kind of potent, vicious satire that produces a lingering hangover.

“Little House on the Parody” will be performed again today, August 27 & 28; “The Crazy Locomotive” today, August 26 & 27 (212-279-4488).