Forget Romeo and Juliet — or, in song-and-dance parlance, Tony and Maria. The American musical theater is full of colorful odd couples. Sweeney Todd fields the homicidal title character and his flirtatious conspirator in mayhem, Mrs. Lovett. But perhaps no pairing is as bizarre as Side Show’s Daisy and Violet Hilton, who are, in the most physical way, stuck on each other. In a month when it seems everything’s coming up musicals, both arguably grotesque pairs make appearances on local stages that seem barely large enough to contain them, demonstrating in the process that, though the pain of love is sharp, a well-stropped razor is sharper.

New Repertory Theatre bites off a particularly large mouthful with what many consider Stephen Sondheim’s masterpiece, the near-operatic 1979 "musical thriller" Sweeney Todd, the Demon Barber of Fleet Street. Fortunately, the troupe find it easier to chew than one of Mrs. Lovett’s meat pies (the only things harder than which, in the show’s predatory 19th-century London, are "the times"). Director Rick Lombardo crams 24 singer-actors and six musicians onto several tiers of a tiny stage off which the show spills into a likewise intimate house of fewer than 150 seats. Given the tight quarters, the Sweeney of Todd Alan Johnson (who during his "Epiphany" leaps down a whole staircase, his hollow eyes on fire) seems truly larger than life. And when he slits a throat, then uses his fancy tonsorial chair to eject it into a chute that takes it to Mrs. Lovett’s kitchen to become pub food, you fear the skinnier victims may slide right into the audience.

One might question whether the space is too intimate for the melodramatic Sweeney, with its brandished razors and thundered pronouncements that "the history of the world is who gets eaten and who gets to eat" — whether there is in fact a place for petit guignol. But the small surrounds eliminate the need for heavy amplification, allowing us to hear real voices, and the staging, despite some crowding and a turntable that needs oiling, doesn’t stint, squeezing in everything from that murder machine of a chair to a red-glowing oven big enough to braise Hansel and Gretel.

The cautionary tale of Sweeney Todd, which adds psychology and Brechtian social commentary to what amounts to a 19th-century "penny dreadful" about a mad barber, is flagrantly simple. The former Benjamin Barker escapes from prison in Australia and returns to London to wreak vengeance on the evil judge who had him transported in order to move in on his wife. Returning to his old digs after an absence of 15 years, the barber finds landlady Mrs. Lovett has kept his razors but has bad news regarding his wife, who took poison, and his daughter, who is now a ward of the judge. From directed revenge, the anguished Todd sinks into a crazed and general misanthropy that proves fodder for Mrs. Lovett’s pie business.

But Sondheim’s score, which alternates between haunting melody and edgy recitative and is layered with leitmotiv, is breathtakingly complex. Often the gruesomeness of what’s going on is inversely proportional to the beauty of the music, with, for example, Todd gearing up to cut Judge Turpin’s throat as the two sing the lush praises of "Pretty Women." And the score is rendered respectably if at times stridently here, with Johnson and especially Nancy E. Carroll, as the pragmatic landlady sweet on "Mr T," hitting highs of nihilism and tripping comedy even as they sink to bloody and nutritive lows.

Early on, Johnson’s Sweeney seems so overwrought, you fear you’ll get sick of him, even before he crosses over to the dark side of bonkers. But his bitterness leavened by Carroll’s cleaver-wielding coquette of a Mrs. Lovett, Johnson can turn deliciously, evilly droll. And the first-act finale, the irresistible "A Little Priest," in which Sondheim pops masterful jokes and rhyme into a song about baking professionals into pies, provides an opportunity for the kibitzing twosome to dine out on sex and death. Carroll in particular is a revelation, as light on her feet as Mrs. Lovett’s pies are leaden, her straight-tone singing pleasing without being gaudy.

At the next tier of casting, things are more mixed, though musical director Janet Roma manages a decent approximation of the score with her band of six seated aloft of London behind a bit of hung laundry. Paul D. Farwell sings well and is a reptilian Judge Turpin. Robert Zolli as his hearty Beadle rises to the silky delicacy of "Ladies in Their Sensitivities." Leigh Barrett brings her strong, full tone to the increasingly frantic Beggar Woman who turns out to be more, and Austin Lesch, though hampered by several bad wigs, is a sweetly Dickensian Tobias. In the young leads, the sailor Anthony Hope and Sweeney’s imprisoned adult daughter Johanna (namesake of one of the show’s loveliest melodies), Brent Reno and Liane Grasso prove abler singers than actors, but their parts are wooden. And the ensemble, juggling their difficult, dissonant harmonies, manage to sound authoritative and look threatening, in the case of Everett O’Neil even while admonishing the spectators to turn off their cell phones.

Side Show is hardly the milestone that Sweeney Todd is. Still, the 1997 musical, which lasted only 91 performances on Broadway and lost the Tony Award to the turgid Titanic, is worth more than the adjective Lyric Stage director Spiro Veloudos attached to it in his opening-afternoon speech, which was "interesting." Veloudos was being uncharacteristically delicate since Side Show, which was inspired by the real lives of conjoined twins Daisy and Violet Hilton, who became vaudeville attractions in the 1930s, deals with whether sexual love is a realistic possibility for people who can’t go to bed without their sibling.

Indeed, the show, most of the first part of which deals with the rescue of the Hiltons from a seedy carnival by a couple of show-biz hustlers who become their managers, gets unhealthily obsessed in act two with its "doubleheader" romance theme. But Side Show boasts a compelling story and an emotion-driven score (by Dreamgirls composer Henry Krieger) that’s enhanced by novelty numbers delightfully suggestive of the period. And the Lyric, which has surprised us before with elaborate stagings (whether campy, as with When Pigs Fly, or sophisticated, as with Sunday in the Park with George), does it up handsomely. Ace costume designer Gail Astrid Buckley in particular must be exhausted enough to require a spa stay.

Despite the conflict built on whether the Hiltons will acquire husbands as well as stardom, the musical’s central relationship is that of the sisters themselves. Joined at the hip, these are women who can’t get away from each other except in their dreams (as we hear in the musical spat "Leave Me Alone"). At the Lyric, Daisy and Violet are played by veteran Maryann Zschau and newcomer Susan Molloy, who hardly look alike and aren’t even close to the same age. Somehow it works, in part because the characters are meant to be distinct, in part because the actresses are so natural, even tender, in their entanglement. Buckley’s upwards-of-a-dozen mostly flattering matching dresses and a series of look-alike wigs help, as does the way the actresses’ rich, country-tinged voices blend. And though the choreography for the twins is necessarily more kewpie than Contact, Zschau and Molloy prove mistresses of saucy synchronized gesture, giving new meaning to dancing cheek to cheek.

Zschau is Daisy, the more ambitious twin, prone to show-biz dreams and quick retort; the saucer-eyed Molloy is Violet, who shrinks from the spotlight and yearns for a picket fence. In the beginning, the two are the only genuine oddities of a Depression-era freak show run by "The Boss," who’s not above putting the two (and their "connection") on private display. Aspiring musician Buddy Foster brings talent scout Terry Conner to see the girls. Taking along the Hiltons’ African-American protector, Jake, Terry and Buddy rescue the twins and mastermind their careers, which move from vaudeville to the Follies to the Texas Centennial, where, before a bitterly ironic ending, one twin is scheduled to be married Super Bowl–style.

At the Lyric, the three men playing Terry, Buddy, and Jake are fine singers, and each gets his musical close-up. Christopher Chew’s suave Terry has a Phantom-like "Private Conversation" in which he imagines passion with an unattached Daisy. Peter A. Carey’s easygoing Buddy softshoes through the bouncy vaudeville turn "One Plus One Equals Three" (it’s about the romantic triangle of "my baby, her sister, and me"). Brian R. Robinson’s soulful Jake headlines the gospel-flavored "The Devil You Know" — in which the freak-show family weigh in on whether Daisy and Violet should vamoose — and reveals his true feelings on the poignant "You Should Be Loved." Some of the Side Show score is generic, but it’s pleasing and makes able use of recitative. And it’s well played here by an unseen orchestra led by Jonathan Goldberg. Moreover, the rock-flavored ballads for the Hiltons, including the bookended "Who Will Love Me As I Am?" and "I Will Never Leave You," manage a tricky combination of fervency and cleverness. So does Veloudos’s stylish staging, which, like this unusual show, has heart and wears it on a lavishly well-turned sleeve.