Misuse (noun or verb) implies use of something in a way different than intended.
Abuse (noun or verb) has multiple meanings. See http://www.m-w.com/dictionary/abuse
Abuse may include violence, but does not necessarily imply violence.
Child abuse means mistreating a child. Often it refers to sexual abuse. (The schoolteacher was arrested after several reports of child abuse. Or: The girl was removed from her parents' custody because of child abuse, after the parents refused to let their child be treated for cancer and tried to cure her with prayer instead.)
Abuse of a spouse would probably include violence, for example, hitting one's wife. (If your husband is being abusive, we have safe shelters for victims of abuse or domestic violence.)
It can also be verbal. (The customer heaped abuse on the customer service representative.)
A person can abuse drugs. (The substance abuse clinic at the hospital treats people with problems of alcoholism, drug addiction, and drug abuse.)
Self abuse (an old fashioned term) usually means masturbation.