The worst damage was caused by a twister near the town of Shawnee, 35 miles (55km) from Oklahoma City, local media report.
A mobile home park near Shawnee is said to have been razed. Tornadoes, hail and high winds also hit Iowa and Kansas, part of a storm system stretching from Texas to Minnesota.
The National Weather Service (NWS) warned of a dangerous tornado approaching the city of Wichita, Kansas. It had earlier issued urgent appeals for people in parts of Oklahoma to take cover.
‘Wiped out’: In Oklahoma, a tornado smashed a trailer park on Highway 102 near Shawnee.
The body of a 79-year-old man was found out in the open afterwards, the Associated Press reports. A Fox25 reporter in Shawnee said trees had been shredded and homes destroyed. Downed power lines were seen lying on roads.
Sheriff Mike Booth said: “It’s pretty bad. It’s pretty much wiped out.” One resident, Amber Ash, said her home was hit by a tornado as she waited in a storm shelter.
“Once it passed, we got out and saw the devastation. Everything I had was destroyed.” There was also serious damage in the town of Edmond but no injuries were reported. Thousands of residents in the affected areas have been left without power.
Gov Mary Fallin said a state of emergency had been declared in 16 counties to enable help to get to the worst-hit parts of Oklahoma.
At least four tornadoes ravaged the state on Sunday, part of a storm system that was moving north-east across the Midwestern states and Texas. “Right now we’re in a rescue and recovery stage,” Gov Fallin said. “We’re still not in the clear yet.
The massive storm system prompted the NWS to issue a blunt warning to residents in the affected states.
The agency said: “You could be killed if not underground or in a tornado shelter. Complete destruction of neighborhoods, businesses and vehicles will occur. Flying debris will be deadly to people and animals.”
Meteorologists warn that the extreme weather is expected to continue on Monday.