Buried beneath a shlubby wardrobe and a sulky demeanor, Catherine Keener drags herself through “War Story” like one of those exhausted mothers in a missing-child movie. What her character has lost, though, isn’t her offspring — it’s her marbles.

As Lee, a traumatized American photographer who has taken refuge in a Sicilian hotel after a harrowing trip to Libya, the doughty Keener is rarely out of our sight. Baggy-eyed and ashen-faced, Lee turns her room into a bunker, licking her wounds and ignoring her incessantly ringing phone. Why she doesn’t just turn it off is only one of this film’s many annoyances.

Aiming for a moody portrait of psychological distress, Mark Jackson directs with a sluggish pace, an abstract style and a dismal aesthetic that rebuff involvement. Releasing information in stingy dribbles, he shadows his tormented heroine as she creeps around the hotel and loiters near a Muslim detainment camp.

Things brighten (at least for anyone who enjoys an actual story) when she becomes involved with a pregnant Tunisian migrant (Hafsia Herzi) who’s desperate to escape both Italy and motherhood. But whenever the script comes close to touching on anything interesting — like Italy’s treatment of immigrants — it shies away to pursue yet another of Lee’s mopey walkabouts.

It’s all quite trying. By the time Ben Kingsley, playing Lee’s mentor and former lover, pops up momentarily to note that she’s a little nutty, it’s too late. That’s one of the few things we already know.