Most deaths occurred before the cyclone made landfall Saturday night, as trees uprooted by strong winds fell on unsuspecting people.
Heavy winds felled hundreds of trees in the entire coastal belt.
The deaths were reported from Khurda (2), Ganjam (2), Puri (1), Balasore (1), Bhubaneswar (2), Behrampur (3) and Jagatsinghpur (1).
The NDRF said 865 km of roads had been cleared of fallen trees and electric poles.
A total of 83 people were rescued from Kavitri Mandal, Ganjam and Jagatsinghpur.
Southern Odisha bore the brunt of the devastation as large swathes of low-lying areas were submerged following hours of heavy rains. The strong winds also blew away thatched houses.
The administration had evacuated more than half a million people from the low-lying areas of the state, especially those in kaccha or mud houses.
"We could manage to save human lives because the people were evacuated beforehand," Surya Narayan Patro, Odisha's revenue and disaster management minister, told IANS.
"It is certain that there has been severe damage to property which we are in the process of evaluating," he added.
In Andhra Pradesh, around 1,000 people trapped in a village in Srikakulam district were rescued.
Relief and rescue operations are in full swing in Andhra Pradesh including in Srikakulam, Vishakapattnam, Vijaynagaram, East Godavari and West Godavari districts.
No casualties were reported from Andhra Pradesh.
In view of the heavy rains forecast for Bihar and Jharkhand, three NDRF teams have been deployed at Supaul, Sitamarhi and Darbhanga and two are being sent to Patna.
In Jharkhand, two teams are positioned at Ranchi and Dhanbad.