Something is broken if it is so badly damaged it can't be used for its original purpose. For example, a chair is broken if a leg has come off and you can't sit on it. The cup in the picture is shattered so badly it no longer holds coffee. Some things that are broken can be fixed, but not all.
Something is corroded if it is showing damage from being slowly eaten away. Many metals become corroded over time by a slow chemical reaction. Iron becomes rusted as it corrodes.
A crease is a line that has been made in a surface, usually by bending or folding it. People get creases in their skin in places that move, like around their eyes. The piece of paper in the picture has creases in it from where someone has folded it into the shape of a paper plane.
Damage is some kind of harm that is caused to something else, which doesn't completely break or destroy it but does reduce its usefulness or value.
The tomato in the picture has been damaged by birds.