Can a mega-tsunami have a height of 30,000 feet or more? Is it possible on Earth?
Roughly what size would an impactor have to be to cause a tsunami of this height? And it's speed, energy equivalent in tons, megatons, etc.?
 A: The Chicxulub crater was created by an asteroid and is estimated to have produced around $10^{23}$ Joules of energy, roughly 100 teratons of TNT! The largest bomb we've created is 57 megatons, one-two-millionth of that value! So surely we cannot do it. The largest volcanic eruption on earth occurred in America and produced only 0.25% of the energy of the Chicxulub crater.
The waves produced by that asteroid have been estimated to be around "a few kilometers" which is about a third of the height (9,800 ft) you are questioning. The asteroid that caused this was around 10 km (33,000 ft) in diameter, so we'd need an asteroid that was significantly larger to generate a wave that was 30,000 ft.
A: No - tsunami's are more like flash-floods than normal waves that rise high and then break. There are videos of that Japan tsunami from a while back where you can clearly see that behaviour.
To cause a tsunami by means other than an earthquake you need a kilometer-sized asteroid, a supervolcano or a massive landslide (there's a volcano that may do this in the future - I forgot where it's located).
__
You can of course try to put a lower limit on the energy of an asteroid impact by calculating the amount of energy required to rise the water by such an amount.
Assuming it splashes in the middle of a the Atlantic it will travel $2000 $ km.
We're going to raise an amount of water $h = 9000$ m high, with a base of twice that and a width $w = 2 \pi (2*10^6)$ m (a pyramid shape). A slice of that would weigh $\rho w(2h-2z)dz $ kg. The work to raise it a distance $z$ is then $dW=g\rho w(2h-2z)zdz$.
The total work is  $W= g\rho w  \int_0^h (2h-z)zdz = \frac{2}{3}g\rho wh^3$. Plugging in our values gives $6*10^{22} $J . For scale, that's about 100 years of global energy consumption.
An asteroid hitting Earth is going somewhere between 11km/s and 42km/s. It will have mass of at least $6.8*10^{13}$ kg, and a diameter of about 4 km.
Obviously since we've ignored many things, such as raising from sealevel, heat, wave attenuation, shockwaves and more, it's going to be at least ten if not 100 times as big.
A: Water surface waves break when their amplitude becomes too large; in shallow water this happens when the wave height is larger than 0.8 times the water depth. A 30,000 feet wave will experience most ocean (with the exception of the deepest trenches) as shallow, and since the average depth is just 3,688 meters it would break.
One can certainly imagine enormous impactors, but the problem is that when we approach giga-tsunami sizes it becomes less and less clear that it is a tsunami. A big shockwave can push a wall of water forward: does that count as a tsunami? Powerful impacts may produce a seismic wave mixing rock and ocean, does that count? If we define tsunamis as ocean waves that only progress by ordinary hydrodynamics, then the wave in this question will cease to be a tsunami. 
A: There is evidence of a massive tsunami in the form of thousand foot high chevrons composed of sea sediments in Madagascar and western Australia.  Some scientists believe that the Burckle crater in the deep Indian ocean may have been caused by an object 3-5 kilometers wide.  Based on limited data from early and prehistoric astronomers one researcher has pegged this to possibly have occurred in 2807 B.C.
The Burckle crater has never been studied (partly because it is nearly three miles deep) to see if its origin confirms this theory.
