The victims were sleeping when a mini truck carrying straw lost control and overturned on the house.
The injured were rushed to Shaktinagar hospital where three were declared dead on arrival.
The victims have been identified as Phulkali Hansda (34), her sons Patal (8) and Indra (3). The woman's eight-year-old daughter Bulbul was undergoing treatment.
While police seized the truck, which was on its way to Krishnaganj in Nadia from Burdwan, the driver managed to flee.