Oscar night is upon us, and while the smart money favours Martin McDonagh taking at least one golden man home for Three Billboards Outside Ebbing, Missouri, what many forget is that it won’t be his first. Having won in 2006 for his mordant half-hour death study Six Shooter, McDonagh joins Andrea Arnold, Peter Capaldi and Jean-Claude Carrière on the motley list of Oscar champs in the short film categories – largely overlooked each year because the nominees have been so hard for audiences to access.

The advent of online viewing has done much to change that in recent years, though: gone are the days of having to predict the short-film winners based on which title you most like the sound of, or which one appears to be even tangentially about the Holocaust. Thanks to leading online short-form platform ShortsTV, this year’s nominees for best live action, animated and documentary short are available for download via Amazon Video – and it’s a compellingly varied pick-and-choose buffet, with a number of titles of interest to more than just obsessive Oscar completists.

Only that group need bother with Dear Basketball, an icky animated tongue-bath of an ode to NBA star Kobe Bryant – written, as it happens, by NBA star Kobe Bryant – even if it is widely tipped to win, overcoming lingering sexual assault allegations against Bryant in the process. But everyone should seek out the corresponding frontrunner in the live-action category, Reed Van Dyk’s DeKalb Elementary, and not just because the cloud of recent events in Parkland, Florida make this stark, sober two-hander between a teenage high-school shooter and a terrified but coolly empathetic school secretary particularly throat-grabbing. Gutsily acted and freezingly tense without dipping into sensationalism, it’s a bare-bones 20-minute affair that lingers longer in the mind than some of this year’s best picture nominees.

It’s the best of several shorts on this year’s slate addressing America’s current maelstrom of social crises. The short categories are usually where international cinema gets to compete on equal footing with US fare, but unless the japey, clever-cleverness of Australian entry The Eleven O’Clock – an amusingly ambiguous shrink-versus-patient riff – triumphs on the basis of its tonal light relief, it seems like a solemn, inward-looking year. The two strongest entries on the documentary side follow suit: Traffic Stop is a bleak, seething account of an African-American woman’s mistreatment by white policemen in response to a minor traffic arrest, while Heroin(e) transcends its corny title with its tough-minded, process-fixated portrait of three women battling an epidemic of drug overdoses in their West Virginia town.

Even my favourite of this year’s animated nominees, Max Porter and Ru Kuwahata’s Negative Space, is far from a romp. (Though if that’s what you’re after, Garden Party, an impressively photo-real frogs-on-the-loose jamboree, does the job to eye-popping, toe-tapping effect.) But Porter and Kuwahata’s gorgeous slip of a heart-tugger, detailing the relationship between a son and his oft-absent father through a pragmatic suitcase-packing tutorial, shows just how much a movie can get under your skin in a mere five minutes. It’s a medium we still give unduly, well, short shrift, and I’m as guilty as anyone: the Academy Awards shouldn’t be the one occasion a year to draw film lovers’ attention to non-feature cinema, but they’re a good place to start.

Also new to streaming & DVD this week

Armie Hammer (right) and Timothée Chalamet in Call Me By Your Name. Photograph: Sony Pictures Classics/ Sundance

Call Me By Your Name

(Sony, 15)

Speaking of the Oscars, if you haven’t caught up with the woozy, winter chill-beating pleasures of Luca Guadagnino’s lovestruck best picture nominee, you can now do so at home.

The Killing of a Sacred Deer

(Curzon Artificial Eye, 15)

Or bring the chill irrevocably indoors with Yorgos Lanthimos’s headily brilliant, black-hearted contemporary twist on a Greek tragedy.

Thelma

(Thunderbird, 15)

Now available to stream on Mubi, Joachim Trier’s queer Nordic riff on Carrie got too little attention in cinemas: it’s cool and delicate and brittle as frost on a windowpane.

Yi Yi

(Sony, 15)

The most geekishly awaited Criterion Collection edition in some time: a lavish package for Edward Yang’s vastly encompassing but minutely detailed Taiwanese family epic.