Can I take him to court for slander libel or harrment?

Well I have an ex boyfriend. We broke up back in april and he has been totally unstable ever since. One day he would tell me he loved me and missed me and the next would be sending me emails threatening to kill me and my family. I filed a claim with the police department about those emails and i still have them. Because his emails stopped after that i took no other actions. now he found out that i am with someone new and has been emailing him and sending him messages on facebook calling me a telling him im only using him and i have an STD ive been spreading around and so many more lies. Is there anything i can do to stop this?