How strong does an earthquake need to be in order to cause a Tsunami?
It varies. The size of the quake is only one factor. Others are the shape of the sea floor between the quake and the land, the distance from the shore, the depth, and a dozen other things.
New Answer: All of the above is very true, but many seismologists believe an earthquake of at least 6.0 magnitude is required to generate a tsunami, but of course not all earthquakes above this magnitude will generate a tsunami, even if they occur under the ocean. However, it is mainly a factor of the amount of displacement in the ocean crust as a result of the earthquake, rather than the amount of energy is released by it, as this is what causes the tsunami wave.
New Answer 2: Seafloor movement is only one means in which an earthquake can generate a tsunami; a relatively minor earthquake (or even no earthquake) can trigger a massive landslide on a steep, already-teetering slope, and the tallest recorded tsunami in history were generated by landslides (such as the wave caused by the landslide triggered by the May 18, 1980 eruption of Mount St. Helens into Spirit Lake, estimated to have triggered a wave that reached some 1,500 feet in height; a similar tsunami at over 1,700 feet was triggered by a landslide not even associated with an earthquake nor volcano in Alaska on July 9, 1958. A tsunami could also be generated by a meteor striking the ocean or a lake.