One appliance and crew from Thame, one from Aylesbury and one from Kidlington attended, along with an officer.
The collision had occurred close to the Bottle and Glass pub, Gibraltar Village.
The 3.5 tonne lorry was lying on its side in the road.
One man and one woman were out of the car before the firefighters arrived.
The firefighters provided immediate emergency care to a second woman and used hydraulic rescue equipment and a short extension ladder to release one man who was injured.
The incident was left in the hands of South Central Ambulance Service.