Should I get rid of this weird friend?

This girl who I'm friends with is very strange. She talks to random people and just blurts out inappropriate stuff. This weekend, she stayed the night at my house and it drove me crazy. She was clingy, every time I sat on the couch, she would sit on top of me, When we went to the mall, she followed these group of kids who she didn't know from atom. I no choice but to follow her. And when I tried telling her that my mom wanted us to leave at a certain time, she kept trying to be friends with them. She even went as far as sitting on their laps. What's even worse is that she embarred me at a football game by screaming at my old friends and even calling my friend a "blonde bimbo". Then she added all of my friends on Facebook, wrote on their walls asking if they remembered her, and she didn't even know them! And I could have sworn she was in my bed, because during the night I kept hearing "squishy" sounds and when I looked over, she had her hands near her face. I'm sorry, but I don't think I can deal with this. We go into the store to buy some clothes and she tries to go in the dressing room with jewelery. Everyone knows you can't take jewelery into a dressing room!. Oh, and last but not least, when I told her my grandpa was from Kentucky, she asked "Is he a redneck!" I know she needs a friend and all, but now I see why she didn't have many friends to begin with. She's a very unusual girl with deplorable social skills.