By Melinda Miller

The 1982 movie “Star Trek II: The Wrath of Khan” is an exquisitely cheesy sci-fi romp and so it’s no surprise that “Khan!!! The Musical!” is also rich with the cheddar. 

The “Khan!!!” show – a “parody Trek-Tacular” – now onstage at Shea’s Smith Theatre deserves every one of its exclamation points. Creator Brent Black has deftly lifted only the best ingredients from both the “Star Trek” and Broadway universes to concoct his multiverse-mashup. Presented by O’Connell & Co., director Daniel Lendzian serves it up with giddy style. 

Deftly avoiding dark (and blue) matter, this ship boldly goes where all Trekkies have probably gone many times before, to the desolate planet Ceti Alpha V, where they once again accidentally rescue the most popular villain ever to cross swords with now-Admiral James T. Kirk.

The villain, of course, is Khan Noonien Singh, first seen – and exiled – on the original 1960s TV series and memorably resurrected for the movie by the incomparable Ricardo Montalban and his pecs. 

In the decades since, much discussion online and elsewhere has centered on whether Montalban, famously fit but in his 60s when he made the film, was wearing a chest prosthesis. (No.) The debate does not go unnoticed in “Khan!!!,” with the diminutive Len Mendez using all the help he can get to enhance Khan’s revenge-driven stature. (Props to costumer Timmy Godman for this and the rest of the Trek uniforms.)

The premise for the musical is very of-the-moment. The show opens with Data (Joe Greenan), the android from “Star Trek: The Next Generation,” explaining that he has cobbled together a show by studying Broadway and starship history. 

In other words, he uses A.I. to swipe ideas and call them his own, a process later cheerfully acknowledged as “blatant song theft” and plagiarism. 

“I believe I’ve just become a composer!” he celebrates.

He also has no bones about casting himself in his own show, which is “full of historical inaccuracies, ’cause “It worked for former President Lin-Manuel Miranda!”

From the intro we move at warp speed to cadets trying to solve the infamous and unsolvable Kobayashi Maru, in song, before turning to the middle-aging Kirk, lamenting his now-boring life. 

Though he looks nothing like William Shatner, John Kreuzer takes the role like he’s already in the captain’s chair and, under an outrageous hairpiece, runs away with it, clipped dialogue and all.

Opposite him is Vinny Murphy as Spock, whose impending melodramatic doom is foreshadowed repeatedly; Ashleigh Chrisena Ricci is the Vulcan trainee Saavik. 

They are joined by a fine chorus of musical talent, including Christopher Wagner as the grounded Dr. McCoy, Dasia Cervi as Uhura, Miguel Gutierrez as Sulu, and Nick Lama as Scotty. 

Audrianna Yates plays Kirk’s former love interest, the brilliant Dr. Carol Marcos, and Greenan also plays her/their son David, also with a Shatner imitation; Steve Maisonet and Taylor Lee Hall are versatile crew members.

Joey Bucheker, who plays Chekov, did the futuristic choreography, which includes jazz hands and tap shoes, along with a Muppety bunch of singing chickens – a little gift for those who were hoping for tribbles.

And there’s another gift: O’Connell & Co. announced they have added an extra show, extending the two-week run to Monday, Jan. 27. 

The remaining performances are Jan. 23, 24 and 25, plus Jan. 27 at 7:30 p.m., and Sunday, Jan. 26 at 2 p.m. Shows run about 2 hours and 15 minutes, meaning the Sunday show will end well before kickoff for the AFC Playoff in Kansas City. 

Tickets are $45, $35 for students, at sheas.org.