In basic, all are similar to each others because they are meant "somethings become worse or demaged" at all.
Here some series of explanations of meaning and examples for your reference!
* 破坏= break down; destroy;
Example: Wood-cutting destroys the natural environment. Please stop!
* 损坏 = demage; impair
Example: My father's hearing was impaired by an accident.
* 损害 = injure; damage; loss
Example: Over-smoking has injured your health! Hope you quit smoking from now on.
Hope these make you clear more!