The two women were sleeping in their house at Pahana village in Kujanga when an overhead wire fell on their house after getting snapped and one of them touched it.
The other woman tried to save her and too died of electrocution, the police said.
"On hearing the scream of other members present in the house, their neighbours attempted to stop the main switch but got died," inspector-in-charge of Kujanga police station Gupteswar Bhoi said.
All the six were taken to the nearby government hospital at Kujanga where four of them were declared brought dead. The injured including a child were undergoing treatment and their condition was stated to be critical.
The victims were identified as Koili Patnaik (70), Saraswati Patnaik (30), Kesaba Patnaik (60) and Pramod Patnaik (25).
Meanwhile, in protest against the incident, irate villagers today gheraoed the local electricity supply office and demanded compensation.