The mishap took place as the vehicle dashed against a culvert railing when the victims from Belgharia in West Bengal's North 24 Parganas were proceeding to the seaside pilgrim town of Puri, police said.
While the man, identified as Manoj Kumar Dey (46) died on the spot, his son Mirzanka (10) succumbed on way to hospital, the police said.
The woman was admitted to a hospital in Bhubaneswar for treatment where her condition was stated to be serious.