A shelter is being opened at the First Baptist Church of Elk City to help affected residents.
Fitzgerald says many emergency crews are on hand.
Officials with the National Weather Service say survey teams have discovered damage that leads them to believe the tornado was at least an EF-2.
The weather service's Storm Prediction Center in Oklahoma said storms with the potential to spawn tornadoes and dump large hail stones could hit the region Thursday.
The National Weather Service has received scattered reports of tornadoes among the severe thunderstorms rumbling Tuesday afternoon over the Texas Panhandle and western Oklahoma, downing power lines and toppling utility poles but having little other effect.More news: HTC Vive reveals standalone VR headset
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Bynum, 48, said he was doing what many people do when the weather picks up: watching it in his yard. Shards of glass were flying at them like bullets, Tyson told the Eau Claire Leader-Telegram.
More severe weather is expected in parts of the Midwest a day after tornadoes killed two people and destroyed dozens of homes in Oklahoma and Wisconsin.
The Red Cross says dozens of people who lost their homes when a tornado leveled a trailer park in northwestern Wisconsin are staying with relatives or friends while others are using donated hotel rooms and a temporary shelter.
Manning said the same tornado that came from the southwest hit the Elk City housing addition Fairway near the municipal golf course.
Several poultry barns at a turkey processing plant across the street from the trailer park were badly damaged, and turkeys could be seen wandering in the debris. Emergency services are continuing to rescue Elk City residents, several of whom remain trapped under the rubble of their homes. Authorities said it appears he was fleeing his home when his vehicle was thrown several hundred feet. But Fire Chaplain Danny Ringer told reporters at the scene late Tuesday that one person was known dead from the twister.