“Rock Me Sexy Jesus.” “You’re As Gay As the Day is Long.”

These aren’t insults. They’re song titles from the new film Hamlet 2, which opens tomorrow.

The movie follows an eternally optimistic but marginally talented high school drama teacher as he mounts an ambitious musical sequel to Hamlet that he hopes will save the school’s drama department. The irreverent songs come as choreographed musical numbers in the student production, which closes the film.

Director Andrew Fleming, a self-proclaimed lover of musicals, co-wrote the flick and its titillating tunes with South Park writer-producer Pam Brady.

“Because I’d never written songs before, we didn’t know what the rules were,” said Fleming, whose previous credits include Nancy Drew and Dick. “We didn’t know you shouldn’t write about the tasteless things going around in your head.”

Brady got some experience with silly songs when she worked on South Park: Bigger, Longer & Uncut and Team America: World Police, but that was “just a few lyrics,” she said. “I had never really written a full thing.”

Fleming and Brady spent five years writing the Hamlet 2 screenplay. The songs came in a rush just before filming began.

“It was like an accidental panic craziness,” Fleming said.

Though the songs’ titles and lyrics are kooky and crass, they are presented with complete sincerity by drama teacher Dana Marschz (Steve Coogan) and his cast of misfit students. That’s what makes the otherwise acerbic songs sing, Brady said.

“This musical is coming from the mind of Dana Marschz, the teacher, and he doesn’t think it’s funny and he’s not trying to be offensive,” she said. “The joke of it is that he’s so damaged and he’s trying to be so honest with his feelings but he’s so limited with his abilities that it ends up being completely inappropriate.”

A trio of teenage girls bob their heads as they sing “Rock Me Sexy Jesus.” “He’s the son of God and I think that’s cool,” they chirp. “But he’s got a swimmer’s bod like nobody do.”

The sing-along, happy 1960s vibe of “You’re As Gay As the Day is Long” belies its mostly unprintable lyrics. “You’re as gay as the night is dark,” the whole cast sings. “You’re as gay as a unicorn park.”

In crafting the songs, Fleming said he and Brady weren’t aiming to offend. “It was just what came to us naturally,” he said. “It maybe came out of frustration because we had seen so many musicals and we were trying to do something that was really funny.

“I’m not pretending these songs are as good as any musical ever,” he continued. “I hope people will think they’re a breath of fresh air.”

Coogan said the warmhearted nature of his character is what makes the play palatable.

“However mistaken he might be, he’s really passionate. He’s not cynical,” Coogan said. “He’s trying to do something. He’s trying to make a difference, and that’s what underpins some of the dumb stuff in the play.”