Halloween is more than a month away, but a raucous off-Broadway costume party is already in full swing. Gordon Greenberg and Steve Rosen’s “Dracula: A Comedy of Terrors” has been in development for several years; in 2020, it was adapted into a radio play and performed by a cast that included Broadway stars such as Annaleigh Ashford, Laura Benanti, and Alex Brightman, offering much-needed comic relief at the height of the pandemic.

For the show’s latest, physically staged incarnation, Mr. Greenberg, who is also the director, has recruited a company of rising actors and theater stalwarts, all of whom prove marvelously adept at the frisky, no-holds-barred humor that he and Mr. Rosen have applied to their take on Bram Stoker’s creepy classic. Mr. Greenberg has cited Mel Brooks, Charles Ludlam, and Monty Python as inspirations, and further noted that he and Mr. Rosen were intrigued by how Stoker, “a closeted gay man in Victorian England, play[ed] with sexuality and gender norms.”

The result is a 90-minute romp in which four of the five cast members juggle multiple roles, with men playing women and vice versa, and the titular vampire is depicted as a preening, swaggering, sexually omnivorous hunk — portrayed here by James Daly, a tall, muscular blond with a deceptively angelic face. Hoping to dig his fangs into the virginal heroine, Lucy, this Dracula flirts with her timid, uptight fiancé, Jonathan, who seems riper for seduction.

“Where does she sleep?” the count asks, before quickly correcting himself: “I mean live.” Jonathan, who will later loosen up considerably in Andrew Keenan-Bolger’s canny, endearing performance, seems to find himself drawn to this mysterious Adonis even as he yearns to be worthier of the more spirited, courageous Lucy. 

Jonathan’s better half is played by a winsome Jordan Boatman, who manages deft double duty as the decrepit Kitty, an elderly mental patient-turned-servant and kleptomaniac. Mr. Keenan-Bolger proves just as facile in a handful of smaller parts, notable among them a booze-addled gravedigger.

Veteran troupers Arnie Burton and Ellen Harvey complete the cast in two pairs of gender-bending star turns. Ms. Harvey alternates as Lucy’s father, the smug but well-meaning Dr. Westfeldt, and another one of his charges, Renfield, sometimes transforming from doctor to patient by abruptly shifting vocal accent and timbre or, later, taking off and putting on a wig. 

Mr. Burton plays both Lucy’s involuntarily celibate sister, Mina, whose thirst for carnal knowledge is a source of recurring jokes and gags — “I’ve been riding horses for years,” she tells Dracula at one point, hoping to pique his interest — and a female Dr. Van Helsing, who in the actor’s hilarious portrait suggests a fusion of Dr. Evil and Frau Farbissina from the “Austin Powers” movies, albeit with more heart than either of those heavies. 

Mr. Greenberg and his designers — notable among them Tijana Bjelajac, who crafted the spare set and minimalist puppets, and Victoria Deiorio, who provides both flamboyant sound and mock-spooky original music — maintain a freewheeling, let’s-put-on-a-show vibe that makes these highly skilled performances seem effortless. The script, similarly, throws goofball pitches with a speed and dexterity plainly born of sophistication.

These include, as you may have surmised by now, unabashedly naughty lines, even for the ingénues. Spotting a sign outside one of Dracula’s homes, Lucy reads, “‘Deliveries in the rear — only accepted after sunset.’” To which Jonathan, by now made more daring by an unexpected turn of events, replies, “Kinky.” 

Like some of the scarier moments in more straightforward accounts of Stoker’s monster, such jokes may not be for the faint of heart. Too bad for them, because this “Comedy of Terrors” is a scream.