Lauderdale County Sheriff Billy Sollie told The Associated Press that some of the victims suffered from gunshot wounds. He said he was withholding their names until relatives are notified.
Sollie said the dead man and woman were parents of the children but not married to each other. The boys were 4 and 5 years old.
The man's father, who also was living in the home in the east-central part of the state, found the bodies when he returned from work Thursday afternoon, the sheriff said.
"This is a tragedy for the families involved in our community during this time of celebration," Sollie said in a telephone interview from the crime scene.
Investigators arrived on the scene about 4:30 p.m.
Sollie said some of the dead people had been shot, but he said the cause of death couldn't be determined until autopsies were complete. The bodies were being sent to Jackson, about 90 miles to the west, for autopsies.
The home is outside Meridian in the southeastern part of Lauderdale County, which is on the Alabama line.
The mother's body was found in one room, the body of one child was found in a hallway, and the bodies of the father and the other child were found in another room, Sollie said.
The father and grandfather had been living in the home for some time, and the mother and children appear to have been living in the home about a week, the sheriff said.
Sollie said he did not expect to release the names of the deceased Thursday night. He said it was too early to say who committed the killings.