What would it feel like on Earth if the Earth accelerated due to sudden changes in the solar system like ejection of another planet? Would there be giant tidal waves and other cataclysmic events?
We wouldn't feel the ejection of another planet off the solar system, since the attractive force of distant planets to Earth is very low.
Only close encounters of Earth with other planets would cause noticeable up to severe changes on Earth. This would be caused mainly by tidal forces due to different acceleration for different parts of Earth, or by changing the orbit of the Moon. A homogeneous acceleration wouldn't cause immediate damage, but with some delay it may cause temperature changes due to the change of Earth's orbit and the changing distance to the Sun.