All three words are very similar. People rarely use the word "maltreat" in speech, but you may see it in writing sometimes. "Maltreat" is pretty much the same as "mistreat." "Abuse" and "mistreat" are also similar, but "abuse" is stronger.
If you say that a mother "mistreats" her son, it means that she does not treat him well. She might be mistreating him in a mild way or in a severe way -- it's not clear. If you say that she "abuses" her son, it sounds like she physically hits him, or says very cruel things to him. Usually, if you "abuse" someone, it isn't mild.
In most cases, all of these words can be used interchangeably, but the word "abuse" creates a stronger mental image of severe mistreatment.