The incident occurred between Rua and Bhailapur on the Nirakarpur-Puri road.
The injured have been admitted to Chandanpur hospital.
The accident took place when the driver of the vehicle lost control, the police said.
The family from Ganjam district was on its way to Puri to visit the Jagannath Temple.
Chief Minister Naveen Patnaik announced an ex-gratia of Rs 2 lakh each to the next of the kin of the victims.