What are your right as a home owner to kick someone who is not paying rent or anything to do with the home?

You have to notify them to leave and if they don't, you have to file an action to evict them. Or, if they are broke, you could wait until they leave, box up there stuff and put it on the front porch. Don't forget to change the locks. You may be liable for damages, but I think they will be minimal.