Mega-tsunami, what is the greatest possible height of a tsunami?
Your question seems to lump at least three different phenomena together: tsunami waves(seismic sea waves), the effects of landslides near the coast, and the effects of asteroid impact into the ocean.  You might have also included rogue waves. Each of these are complex phenomena when you start considering 'realistic' boundary and initial conditions - so you should not expect a highly accurate answer from a simple model.   

Seismic sea waves, or waves initiated by land slide, can travel great distances across the ocean. These waves have a long wavelength and therefore may be modeled as shallow water waves. Although the height of classical shallow water wave may be limited (in theory) by the wave steepness (1:7) where the wave 'breaks' and collapses, Computer models of tsunami are likely to be much more accurate.

If you are primarily interested in what happens near a coastline or in a bay, then the most accurate solution will likely be a computer model that also include realistic boundary conditions. See these computer models of a dam break and waves in an irregular water body.

The possible initial conditions for an asteroid impact could be so large that planetary material is ejected into orbit. The Martian meteorites found on Earth are believed to have originated from a impact on Mars. In a large impact, the height of the rim wall might not be an accurate estimate of the maximum altitude material was actually thrown.