A quirky and offbeat do not adequately describe this unique movie.
If you like movies like O Brother Where Art Thou and Buckaroo Banzai, then you will like this.

Highway 61
(1991)

Pokey Jones is a naive trumpet playing barber from a small town in Canada.  He dreams of visiting the USA, but has never even taken the car out of the garage.  

One morning, he finds a dead body frozen in his back yard.  Jackie Bangs shows up, saying the body is her brother Jeffrey, and she wants to take him to New Orleans for burial.  Pokey agrees to drive her, and they set off.  Unknown to them, "Jeffrey" had sold his soul to the devil, and Satan needs the body to collect.  Satan, driving a black pickup truck, starts after them.  They meet the Watson family, a travelling family of singers, and Jackie steals all their cash.  Satan catches up to them in the middle of the night while they are asleep in a hotel.  He takes the body and burns the car.  Jackie wants to continue to New Orleans, while Pokey decides to head home.  However, from signs on the car, Pokey realizes Satan took the body and heads down to help Jackie.  Jackie is hitching, and who should drive by but the Watson family.  They pick her up, but they think Pokey took the money not her.  The youngest daughter has a distinctive bandage, leading Jackie to realize that the daughter and Jeffrey had both sold their souls.  From the daughter, Jackie learns Satan's address and heads to his house in Baton Rouge.  Meanwhile, Pokey has befriended a motorcycle gang and they take him to Satan's house also.  Pokey knocks out Satan, and they retrieve the body.  

At Satan's house, Pokey realizes that Jeffrey is not really Jackie's brother.  She did not even know him, his name is not even Jeffrey, and Jackie is just using the corpse to smuggle drugs into the country.  They drive Satan's pickup truck to New Orleans.  They split as Pokey realizes he has been used. Jackie takes the body with the drugs away from the dealers. She goes out to the swamp and sets the coffin, body and drugs floating off down the river.  She has realized that Pokey was kind and decent and really cared about her, unlike everyone else in her world.  Pokey sees her doing this, and plays a dirge for the corpse.  

Pokey and Jackie get back together at the end.  

Thanks Joseph!