Staffordshire police were called to the Weaver Hills area in Wootton, near Uttoxeter, after information was given by a member of the public.
Detectives are treating the deaths as suspicious and believe they were all related.
Once identities have been confirmed and relatives informed more information will be released at a press conference this morning. The children, two girls and a boy, were in a black Ford Capri and they are believed to be from the Uttoxeter or Stafford area.
Police said the coroner had been notified, and a Home Office pathologist will carry out post mortem examinations.
Faye Whitefield, from the post office at the nearby village of Ellastone, said: "We knew something was going on, but the area was completely sealed off. "People were talking about it all day, not knowing whether there had been a suicide or a murder."
Her husband John said he had been delivering the Sunday newspapers in the area of the tragedy yesterday when he was stopped by several road blocks.
"I know the lane where the bodies were found - it is a secluded area on the way out from Wootton into the Weaver Hills. Very few people would have realised what had happened.
"Wootton itself is a tiny hamlet with only about 150 people living there, but Ellastone is just up the hill on the main road between Ashbourne and Uttoxeter.
"The main reaction is going to be for those living near the people who died, but it is a terrible shock for the whole village."
Villagers spoke in hushed tones of the number of police cars and ambulances in the area, along with a helicopter.