Disruptive employee

I have an employee that is mad and not getting his way at work so he is sending numerous letters to corporate, CEO, calling OSHA, every health board, etc. and burying me in paperwork since I have to continually respond to his false accusations. It is very disruptive at work. I have tried to talk to him several times but he refuses and every time I approach him or another manager talks to him he writes to HR and says that he is being harassed. He has been fired in the past and brought back because he sued the company claiming harassment.
I know it is part of my role as a manager and it is a small part but I can’t help feeling angry and just frustrated with the whole situation. I was doing good working through models with each situation that occurred but now I am just exhausted with him in general and I feel it is taking away from other work that needs to get done and the 250 other employees in the company.