A two-year-old and a seven-year-old child are among the 14 victims who have been killed by a series of severe tornadoes and flooding in the south and midwest of the US.

Melanie Espinoza Rodriguez, aged two, was killed in Tennessee after she was struck by a metal football goal post that had been blown over by strong wind, while a seven-year-old child, who has not yet been named, suffered a fatal electric shock in Mississippi.

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Another child, a 10-year-old girl, also drowned in Springdale, Arkansas in the gruesome storm.

A woman also drowned after a rushing water swept away her car in Missouri, and a fire chief in Quitman, Arkansas lost his life after he was struck by a vehicle as he checked the water levels in the area.

The governors of Missouri and Oklahoma have declared states of emergency due to flooding, with Missouri Governor Eric Greitens saying that 30 rescues had been made and several residents have been ordered to evacuate their homes.

Fierce tornadoes swept through the east Texan towns of Canton, Eustace and Caney City, which killed another four people, and injured 50 others.

"It is heart-breaking and upsetting to say the least," said Thomas Bernabei, the mayor of Canton, Ohio, in a news conference.

Cutting a path of destruction that was 35 miles long and 15 miles wide, 50 miles east of Dallas, the storms left homeowners distraught as their houses were damaged.

A car dealership in Van Zandt County was demolished in the freak weather, as cars were overturned and flung into the air before landing on a nearby highway.

Parts of Indiana have received up to 20cm of rain in the floods, while some areas in Oklahoma, Missouri and Arkansas have been submerged in floods 10cm deep.

There appears to be even more bad news for the south and midwest, as flash floods and thunderstorms are also forecast for parts of Louisiana, Mississippi and Alabama, the National Weather Service said.