The worst damage was caused by a tornado near the town of Shawnee, 35 miles from Oklahoma City, local media report.
A mobile home park near Shawnee is said to have been leveled to the ground.
Twisters have been reported in other states, including Iowa, Minnesota, Kansas and Illinois.
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.
In Oklahoma, local TV stations said at least one person was killed and several others hurt when a trailer park on Highway 102 near Shawnee was hit.
A Fox25 reporter in Shawnee said trees had been shredded and homes destroyed. Downed power lines were lying on roads, she said.
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.
Oklahoma Governor 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,” Mary 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.
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