Elliott (Harrison Feldman) welcomes and befriends Greta (Bethany Whitmore), the new girl at school, and later professes his love for her, in “Girl Asleep.” (Shane Reid/Oscilloscope Laboratories)

“Girl Asleep” opens on Greta Driscoll’s first day at a new school. With a worried brow and a freckled face, the 14-year-old sits alone on a bench while other kids on their lunch break flit around her, socializing, playing basketball, doing tai chi. Any wallflower will intuitively recognize her pain, suffered in distressed solitude.

Greta (Bethany Whitmore) isn’t alone for long. First, a sweet dweeb named Elliott (Harrison Feldman) asks if she wants to be friends. Then a trio of mean girls with pink lipstick and blue eye shadow invite Greta into their cool clique, although Elliott can’t tag along.

At first, “Girl Asleep” seems like a typical coming-of-age movie, in which the newbie must choose between aligning with the nice dorks or the popular jerks. But the gently amusing tale becomes something more intriguing — and much stranger.

The 1970s-set Australian movie is based on a play, and it’s the first feature for both director Rosemary Myers and playwright Matthew Whittet, who has adapted his own work for the screen. They infuse the story with a good dose of the surreal. It’s sparing at first: The photo of a man smoking on a record cover springs to life, and so does the stonework wall in Greta’s living room, where a boy painted to be camouflaged into the background suddenly steps forward and walks away.

The complication at the heart of the story involves Greta’s parents (Whittet and Amber McMahon), who think the best way for their daughter to come out of her shell is to throw her a 15th birthday party and invite the whole school. It’s any shy kid’s worst nightmare.

That shindig, which begins with a “Soul Train”-style procession followed by a choreographed dance routine, delivers the emotional hell Greta fears. First, the mean girls turn on her, then Elliott professes his love. Worse, a strange hooded creature steals Greta’s favorite possession, a childhood music box, which sends her into the night forest on a dreamlike ad­ven­ture that involves a greasy monster, an ice queen and a helpful she-warrior who packs a powerful punch.

The sequence comes out of nowhere and lasts longer than it needs to, especially when such earthly issues as Greta’s mother’s malaise or her sister’s rebellion are given short shrift. But the wondrous hunt is also capped by a poignant revelation about Greta’s fear of growing up.

The movie has a groovy period aesthetic, both in Greta’s orange-tinged reality and her nightmarish forest world. The design looks like a cross between Michel Gondry and Wes Anderson, although it avoids quirk for the sake of quirk.

The casting is another asset. Whitmore conveys plenty of deep feeling with a quick flash of her sad, scared eyes, and Feldman plays Elliott as a contagiously excited kid who couldn’t keep his cool if he tried. His reaction when first visiting Greta’s house: “You’ve got plastic horses? I can’t believe it! I love plastic horses!”

“Girl Asleep” isn’t easy to categorize. It’s a wild curiosity that shifts on a whim. In that sense, there couldn’t be a better metaphor for the inner workings of a teenage girl’s mind.

Unrated. At Landmark’s E Street Cinema. Contains brief strong language. 77 minutes.