There’s a lot to laugh about in the comedy-musical The Wisemen (at ACT Theatre through December 22; tickets): the story of the Wisemen Law Firm (Goldberg, Frankenstein, and Murray) is an extended riff on “It Ain’t Necessarily So,” focusing in this instance on what you’ve been told about the Nativity. It’s both gleefully profane and absurd, opening with a song-and-dance commercial for their sponsor, the Puerto Rican restaurant La Isla.

In the course of the evening (overstuffed at an hour and forty-five minutes) a simple paternity suit to determine the parentage of the infant Jesus Christ widens to involve the a gangsta Easter Bunny, the Pope (complete with fabulous hat), and Santa Claus, who, naturally, has ties to Big Oil.

Backed by a three-piece band (Bryant Moore, composer/songwriter and musician; Cameron Peace, guitar; and Sam Esecson, drums), Goldberg (David Bestock), Frankenstein (Gavin Cummins), and Murray (Matt Fulbright) try to discover for a suspicious Joseph (Eli Rosenblatt) who exactly Mary (Dorcas Lewis) managed to conceive a child with.

That they do this while singing songs that sound like klezmer, hip-hop, funk, and salsa adds to the show’s charm, along with the cleverness of Moore’s lyrics [Correction: Eli Rosenblatt and David Bestock wrote the music and lyrics], which will have have you hanging on most every word. As directed by Mathew Wright and choreographed by Ricki Mason, it’s at times hilariously inventive (there’s a camel made of stools, a ’60s LSD-tinged number for Lewis, and a daytime courtroom TV show send-up). It also takes awhile to get to its feet, as the law firm members each get a big number to introduce themselves (all are Jewish, but one’s a Ukrainian cowboy and one’s Irish).

I don’t think most Christians would be put off by the show’s indictment of Santa Claus as a consumerist junkie who needs regular toy “fixes” to keep it together, but this isn’t a show about restoring the Nativity to pride of place, either. It turns out that Mary really gets around, and the belabored treatment of this discovery (specifically the interviews with her exes where they reminisce about doing her) eventually begins to feel like someone has issues that musical comedy can’t resolve.

You don’t have to be Christian to find this set-up tiresome. If you’ve heard one joke about virgin birth you’ve heard that one before, and for another, there’s only so much comedy in slut-shaming these days. Another line-walking bit is that of a limp-wristed proprietor who, so far as I can tell, is supposed to be funny because super-fey and yet also slept with Mary. These unfunny, awkward moments mar an otherwise likably dyspeptic show.