It wasn't immediately clear whether the mobile home park was damaged by an actual tornado or by severe straight-line winds.
Part of a gymnasium with 60 to 70 people inside also collapsed in Sand Springs, but no injuries were reported, the emergency agency said.
Utilities companies said that more than 79,000 customers were without power across the state as of late Wednesday night. At least 10 Tulsa public schools were without power, prompting the city to cancel classes for Thursday.
The first of several tornadoes in the area was spotted near Tulsa at 6:02 p.m. (7:02 p.m. ET), according to the National Weather Service, which called it "extremely dangerous" and bluntly warned nearby residents: You are in a life threatening situation."
A tornado also caused minor damage in the Oklahoma City suburb of Moore — the scene of a massive and deadly twister in 2013 that killed 24 people and injured more than 300 others.
Interstate 35 was closed through Moore, where the National Weather Service said overturned cars were littering the freeway in both directions. Moore police Sgt. Jeremy Lewis said officers were checking unconfirmed reports of minor injuries, and a hazmat team was responding to a tanker that had overturned.
"I really can't believe it. You know, we just experienced some of this a couple of years ago," Lewis told NBC station KFOR. "Just so soon — it's difficult."
Tornado warnings continued through parts of Oklahoma late into the evening. NBC station KJRH of Tulsa reported that homes and vehicles were damaged in the nearby town of Mannford. There were also reports of tornadoes in Westport, Oklahoma, as well as Arkansas's towns of Berryville and Clifty.
The storm system that spawned the twisters was racing toward Missouri, Illinois, Kentucky, Tennessee and Arkansas, parts of which were under severe thunderstorm watches through 3 a.m. ET. The system could spread as far south as Dallas, said Greg Forbes, a severe weather expert for The Weather Channel.
As the system moved east of Tulsa, it continued to have high potential to spin off more tornadoes, the National Weather Service said. Baseball-size hail was reported, and the agency warned that it, too, could produce significant damage.
The area is smack in the heart of "Tornado Alley," where on average more tornadoes touch down every year than in almost any other place in the U.S.
"Man, that is a rough place to live as far as weather goes," said Ari Sarsalari, a forecaster for The Weather Channel.