How strong must a tornado be to pick up a shark? Yes, you know where this is going.
There is a good article on this topic by National Geographic: 'Sharknado' Got One Thing Right: Aquatic Animals Sometimes Do Fall From the Sky
One of the first claims the article makes is this:

In real life, of course, sharks don’t fall from the sky. But fish,
  frogs, and alligators do—and scientists think the likely cause is a
  weather phenomenon called a “waterspout,” a term first coined in 1738
  by traveler Thomas Shaw.

It supports this premise with historical anecdotes where people observed various animals falling from the sky due to waterspouts and tornadoes: fish, frogs, even small alligators:

On December 26, 1887 the New York Times reported that Doctor J.L.
  Smith of Silverton Township, Kentucky, saw something fall to the
  ground. And then it started crawling toward him.
...
The good doctor went hunting for more alligators. He found six more,
  "all quite lively and about 12 inches in length."

However, a NWS spokesman says it is unlikely that a waterspout would pick up a shark:

Don't expect any sharks to drop in. "While the tornado is spinning air
  along the surface of the water, it's not necessarily like a vacuum
  where it's sucking up sharks or sucking up marine animals out of the
  depths of the ocean," Vaccaro said. "So odds are the sharks wouldn't
  even be close enough to be entrained in the circulation of the water
  spout in any way, let alone would they be lifted because they weigh so
  much."

Note some of the weasel words: "unlikely," "odds are," etc. What I want to know is this: how strong must a tornado or waterspout be to pick up a shark?
Let us make some assumptions:


*

*The shark is swimming as close to the surface as possible where it is still able to swim and breathe, so the storm should be able to exert some force on the shark and its surrounding water.

*The physical characteristics are a juvenile great white shark: 2.5 m long and a mass of 500 kg. (many of the sharks in the "movie" were on the small side: let us ignore the ones big enough to swallow a human whole)

*This tornado or waterspout is strong enough to lift an object of the given dimensions, even if such storm strength is off the chart.
How strong would the waterspout or tornado need to be?


*

*How strong of a force would the storm need to exert to lift the shark?

*What EF classification would the storm be: if the storm is so strong as to be unclassified, how fast would the winds need to be?
I suspect the answer will have to do with differing air pressures and the suction force (lift) these air pressures can exert (similar idea to an airplane wing), but I only took one semester of physics in college and am not familiar with the specific equations and principles that could explain this.
 A: The mass is not a problem, But the only way a tornado could pick up a shark is that the Shark jumps almost completely out of water like dolphins. Why? 
First you need to understand pressure; There is no vacuum, this means that there is no suction. It's always the higher pressure which pushes the things to the lower pressure. This always happens the easiest way, resulting the strong surface winds. But these wind's surely doesn't rip off anything wide below the surface. The impact is very limited at the surface. Thus though you see frogs and alligators been ripped of by tornados, this is mainly caused by the fact that the Air pressure is able to blow under them. If some fishes have ever been blown out, they must have first become airborne through waves or if some small lake is sucked completely dry.
You might want to think this further; lets take the greatest pressure difference ever measured in Tornado 0.194 bars, this means quite exactly a water pressure of 2 meters. So it can suck 2 m of water "away", and thus anything closer to surface than 2 m could be sucked away, Right? 
NO. as there is no suction, this pressure difference pushes from outside the Tornado-eye, and therefore it pushes the whole water mass causing a Storm surge. But these Storm Surges are mostly much higher than only 2 m, ie. the highes ever measured was in Australia caused by the Cyclone Mahina 1899; 13 m. It's pressure drop could explain only about 1 m of this. From this can be concluded, that the winds are transferring much more water to the hurricane eye than the hurricane is sucking away, and this must result a downwards pushing flow to the sea surface. Thus anything below the surface, will remain under the surface.          
If a shark is ever sucked by a hurricane, it has been living in some small water pool which is sucked dry with the shark. I can't imagine why a shark would ever jump above surface in  storm, as it's fin would indicate the heavy winds above the surface before. Even if this would happen, it's size and very good aerodynamical shape would make it almost impossible to be carried out by wind blow to a hights that could be considered as "falling from the sky." As for this lift, the blow of the wind must be higher than the terminal velocity of the object. The Fins would turn the shark very soon on nose down position, and at this position the shark shaped object might need some 500 km/h wind to remain airborne. So you might experience some shark rolling by the wind at the ground, near some zoo. The physical limits goes here.          
