The National Weather Service said one tornado was racing through areas west of St. Louis at 45 mph.
A tornado warning was in effect until 7 p.m. CDT.
Scores of water rescues
Rescuers pulled people from fast-moving floodwaters in middle Oklahoma on Tuesday and carried them to safety after strong storms swamped the area.
In Payne County, home to 82,000 people, emergency responders have conducted more than 30 water rescues, the board of commissioners said in a news release. Between 6 and 8 inches of rain fell Monday, officials said.
Floodwater closed parts of Interstate 40 in Canadian County, just west of Oklahoma City, after storms hit late Monday and early Tuesday.
In that county, high water was lapping up against homes in a rural area near the community of El Reno on Tuesday morning, and fire departments' swift water rescue teams were using boats to take residents to drier land.
One rescued woman, Tammy Flowers, told CNN that she and some relatives tried to leave their farm with a tractor, but it became stuck. Her son stayed behind, she said, hoping to tend to some cattle.
"It's not good. The water is coming up and it's really deep," she said.
More than 40 water rescues had been performed Monday night into Tuesday morning, Canadian County Emergency Management Director Andrew Skidmore said.
While rain stopped in that area, severe storms still are expected to rake the central Plains, Missouri, Illinois, Arkansas, and parts of Texas and Louisiana.
Residents urged to seek higher ground
Flash flood emergencies were declared Monday night and Tuesday morning in the Tulsa area, where more than 6 inches of rain have fallen in some locations this week.
The National Weather Service in Tulsa urged people in those areas to move to higher ground, with more rain expected.
"We're seeing reports of flooding and water rescues across (northeast) Oklahoma," state emergency management spokeswoman Keli Cain told CNN.
That included the community of Hominy, a Tulsa-area community where more than 200 people were evacuated Monday night because of rising water, Cain said.
Roads in Ponca City, in northern Oklahoma, have turned into rivers, with the local government urging drivers to stay away from the water.
Stillwater Public Schools, in northern Oklahoma, announced schools in the district will be closed Tuesday "due to excessive flooding."
At least 21 tornadoes were reported in four states
At least 21 tornadoes were reported in parts of Texas, Oklahoma, Missouri and Arkansas from early Monday to Tuesday morning, the National Weather Service said.
The police department asked residents to "not get out and drive around."
"By trying to check out the weather you are only putting yourself and the crews in further danger."
In Missouri, where Gov. Mike Parson declared a state of emergency, winds from a severe storm blew over campers in Wheatland and four people were taken to hospitals.
More flooding coming to Plains and Midwest
Because storms have repeatedly hit the same areas recently, a serious flooding threat has developed in the Plains and the Midwest.
About 12 million people were under flood or flash flood watches, including in Oklahoma City and Tulsa; Wichita, Kansas; and Kansas City and St. Louis, Missouri.
Serious river flooding -- including along the already swollen Mississippi River -- also is expected in the central US as another 2 to 5 inches of rain are expected to fall over the region in the next few days.