Firefighters found the body of Cory Finley in the garage under heavy fire debris.
Amber was discovered in the living room next to Buster.
She was taken to Norman Regional Hospital, where she was pronounced dead.
When firefighters arrived, they discovered a fire in the garage that had spread to the attic, with heavy smoke throughout the house at 2605 Richardson Drive, Norman Deputy Fire Chief Jim Bailey said.
Bailey said investigators are working to determine the cause of the fire, which erupted about 3:30 a.m.
Investigators think the fire was accidental, based on evidence they have looked at so far, Bailey said.
Cory Finley's parents, Richard and Brenda Finley, own the house but were out of town when the fire occurred, neighbors said.
A fund to help with funeral expenses has been set up at any Chase bank. The account number is 172181280.