Americans are sometimes surprised when they meet Jacki Weaver. Having seen her in a slew of recent American films, they're not expecting an Australian accent.

"They're surprised about the way I speak," she says. "I've been asked if I was putting it on, as if I was trying to sound like Chris Hemsworth."

At the same time, some of the Australian crew on her latest outing teased her about losing her accent. Last Cab To Darwin, directed by Jeremy Sims, is  "the first film I've done in about 12 where I've used an Australian accent", she says, almost as if she can't quite believe it. "Some of the crew were teasing me, saying that I've lost it, that I needed to stop talking American."

Last Cab To Darwin is a comedy-drama about euthanasia, a good-natured road movie with an unpredictable destination; it is written by Reg Cribb, adapted from his play of the same name, which was based on a true story. Its central character, Rex, lovingly portrayed by Michael Caton, is an outback taxi driver, a man of routine and ritual who has never left his home town of Broken Hill.

He learns that he has cancer, and also discovers that legislation pending in the Northern Territory might give him the opportunity to end his life on his own terms. Rather than share any of this information with his close friends or his partner, Polly (Ningali Lawford-Wolf) – with whom he has a singular, memorable relationship –  Rex says nothing. He decides to hit the road in his cab, determined to make his way to Darwin. The office of a crusading medical practitioner, Dr Farmer (Weaver), is his intended destination. Along the way, he takes a couple of passengers on board, including an engaging, enigmatic young Indigenous man (Mark Coles Smith) and an adventurous British backpacker (Emma Hamilton).

Weaver was determined to be involved, having been in the original play, also directed by Sims. "I'm very attached to it in a sentimental sort of way. I thought, if they're going to make a film of Last Cab I really want to be a part of it." She was involved with the first theatrical production more than a dozen years ago, before her performance in 2010's Animal Kingdom earned her an Oscar nomination and launched a new phase of her career.

"I was in the first table read," she recalls, "and Jeremy made me play 16 characters that first time, because he didn't have enough girls. Then when we toured the play, and we went to about 30 venues, including Darwin, I played nine different characters." One of the few she didn't tackle was the one she plays in the film. In the original theatre production, the doctor was a male character: Cribb and Sims rewrote the film role for her.

She remembers the play as an intense, joyful experience – touring a work that combined a dark subject matter with plenty of laughter.

"It's poignant, but it's also rambunctious and hilarious in parts, and that's always my favourite kind of story, because it's the most authentic reflection of what life is. You know, how you laugh one minute, and cry the next."

Dr Farmer is an interesting presence in the film; in some ways she's not so much a character, more a goal or destination, a set of possibilities. We learn little about her motivation, her past or her present.

Weaver says she had things she wanted to bring to the character, some tangible, some part of her private preparation. "I wanted to make her sympathetic, because in the play Reg and Jeremy were a little harsh on that character, I thought. They didn't give him enough empathy and tenderness. I think she had to be a little less tough than the male doctor was."

At the same time, she felt she needed to respect the character's single-minded focus. "I think it's clear that she's zealous, she's been written that way," and in pursuit of this, she's lost touch with some of the qualities of tenderness.

Weaver came up with a back story for her. "It wasn't in the text, it was something I invented. You always do that as an actor, I think, but it doesn't have to be something you share with the audience. Sometimes it's good for an audience to make their own assumptions, because if you spell everything out for them you might as well just get them to watch a soap opera. It's good to have ambiguity and make people use their imagination."

Thinking about the character she was playing, she says, "I wondered about her sexuality, I think that's an interesting thing to ponder," although there's nothing in the film to give us any indication.

"I think she probably comes from a medical family, and I think that maybe she'd seen a lot of suffering in her time, maybe by having parents who were doctors or nurses. But I think people who believe in euthanasia come from all sorts of backgrounds, and quite often it's because they have seen their own relatives suffer. And as one gets older, one gets very firm ideas about it. I know what I feel about it," although, she adds quickly, "I don't think this is the time to get political."

Since her tour de force role in Animal Kingdom, Weaver has been in no danger of being typecast. Her next Oscar-nominated role, as Bradley Cooper's mother in Silver Linings Playbook, couldn't have been more different from Animal Kingdom's monster matriarch; since then, she's been in movies by Woody Allen (Magic In The Moonlight), Park Chan-wook (Stoker) and Marjane Satrapi (The Voices), as well as TV.

She's recently finished another role that's allowed her to keep her Australian accent, in a film written and directed by Ivan Sen (Mystery Road). It's called Goldstone, and its cast includes Aaron Pedersen, David Gulpilil and David Wenham as well as Hong Kong actress Cheng Pei-pei (Crouching Tiger, Hidden Dragon).

"We lived in those little shipping container things in far-west Queensland, in the middle of nowhere, and I just loved making it," she says. She's not sure how much detail she can go into about the film. "I can't give too much away, because it's a mystery thriller, but I play a tough old broad who lives in the outback: she's mayor of this tiny mining town and runs the place like she owns it," she says.

Back in the US, she has just finished shooting a TV series called Blunt Talk, which stars Patrick Stewart as Walter Blunt, a British newscaster who moves to Los Angeles to host a nightly TV show.  "I play his Emmy-award winning producer, who's also his close confidante. I'm happily married to Ed Begley Jr, but I'm having an affair with a 24-year-old." She laughs. "I'm a bit apprehensive about how his parents are going to react."

Last Cab To Darwin opens on August 6.