Though they all have seemingly same meaning, there is difference in the way they are put in use. They vary the degree of effectiveness in that particular action.(which is to remove something from where it was before). According to my understanding: Erase,Clear,Eliminate,Purge would be the increasing order in their strength . Erase is essentially used while removing something written mistakenly and is done immediately or while the process of work is still on. ex: I realized that i typed wrong spelling of Nicaraguwa. I erased it and retyped it as Nicaragua. Clear: This is something which is having to do with Vision,perception. ex: I cleared all the doubts in his mind as soon as he approached me with humility. The cops cleared the road to facilitate the Prince's safe journey to the Palace. Eliminate: This is more of used when speaking of negative or unpleasant sentences/circumstances. ex: Elimination of Plague required dedication from governments all over the world. Hitler tried to eliminate Jews from the face of Earth. Purge: This is also used mostly while talking about unpleasant or unexpected circumstances. Mostly used in the case of removing something that is not required but one cant help about it as it is not in their hands to stop it from coming. ex: The Doctor purged the bad blood from the patient who is suffering from blood-cancer. ex: The software engineer Purged the unwanted records from the Data base. Hope this helps. :) Regards.

They all mean the same thing and can be used interchangeably. Are you thinking of any sentence in particular?