To duck means to lower one's head or entire body down to avoid something above. It can imply crouching.
To evade means to move significantly in order to actively avoid something, or sometimes is synonymous with avoid if the thing being avoided is constantly moving and it's location is visible or known. This is not a very specific term.
To dodge means to move slightly in order to actively avoid something, and is usually used in contexts where lateral movement is needed.
For the boxing example, B is dodging A's punch.
For the dodgeball example, it looks like B is in the process of ducking. Dodging wouldn't be wrong here but might imply the ball has already been thrown whereas in the pic it hasn't yet.
In both these instances, evading is something the players should always be doing, so it's too vague of a term in either case.