Staging
Staging does not only relate to animation, it is a broad term used also in film and theatre to describe the environment in which the scene takes place. This includes sets and backgrounds, props, use of lighting, camera angles and movement. Staging is more of a directorial tool than specifically an anmation one, as it can also refer to the overall mood of a scene and how this is created by use of the above techniques. Staging could just as easily be called cinematography in this regard as it deals with the scene as a whole and how the emotion of that scene is carefully created.
Squash and Stretch
Squash and stretch is linked to exaggeration, it helps to demonstrate an object or characters mass and therefore helps you to understand its movement visually. When something squashes however, it should retain its mass so that it may retain its context as a shape or character within its own environment. It is used in conjunction with timing to make object behave believably within its own world, and to obey the laws of physics imparted to that world. Usually earth is depicted using Newtons laws of motion and therefore objects obey gravity and move in a 'lifelike' manner.
These images help to demonstrate the retention of mass while squashing and stretching, and how when used alongside timing makes the object behave in a realistic manner.
Timing
Timing is a crucial aspect of animation< and gives meaning to motion. It is the way by which you impart weight, motion and emotion to an object. In technical terms it is the process of working out how many frames an action should take and how far apart these actions should be. For instance if the frames are evenly spaced accross the page then something will move at a constant speed, whereas if you put more frames towards the end, as in the image below, the object will move quickly and then progressivly more slowly, giving it a more realistic motion.
The video below demonstrates how this is used within the context of some animated cycles, walking, running and hitting something with a hammer.