According to police, the bus travelling from Jajpur Road to Keshdurapal in neighbouring Keonjhar district skidded off the road and overturned after the driver applied brakes to save a cow.
The injured were rushed to the Area Hospital at Jajpur Road, of whom eight seriously wounded were shifted to the SCB Medical College Hospital in Cuttack.
The passengers mostly belonged to Keonjhar district, the police said.
The dead were identified as Santosh Kumar Moharana (44), conductor of the bus and a resident of Nuapatana village, Laxmidhar Chakra of Pandua village and Bipin Kumar Routray (17) of Korabandi village.