I have allowed my ex mother in law to store her personal belongings in my garage. I allowed her to use my garage starting in May of this year, and I have told her on more than one occasion these past two months or so that she needs to remove her property from my garage. She has not done so, and she flat out refuses to do so. Am I legally allowed to dispose of her belongings? I do not want to get sued. What are my rights? We signed no lease, no contract for her to use my garage. She refuses to remove her property. If I would get sued for disposing of her property, can I load up her property and leave it at her residence? Please let me know what I should do. I want the use of my garage back.

Legally for you to do so, you have to give her a letter in writing stating that she has x amount of days to remove her stuff from your garage or you will be disposing of it. Check your state laws for how many days you are required to hold on to the stuff.
Then if she doesn't remove it still take her to district court/magistrate
You may be allowed to drop it off at her residence but she may come back and say stuff was stolen if you leave it on the porch or in the yard if she is not home.