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You have a multitude of problems.
First, knowing who the person may be and proving it when an online user ID is used would be difficult.
Second, you can avoid the contact by not participating in that particular newsgroup. If it is an issue with your facebook, you can change your security to deny that person access. You cannot control what that person may say to other people or what that person posts to their own facebook page or on the pages of someone other than you.
WIthout a threat or some direct form of communication - (phone calls, letters, personal visits, text messages emails) - that substantially interfere with your safety, security or privacy, there is little that can be done.
Its causing me a great deal of stress..she posts really nasty things about me and then today she said that SHE went to the sheriff's office and court house in her state...Im very upset because she can take and twist it to make her look like the victim, I do have print screens of some of her nonsense. Im concerned that she is going to use the law to harass me now that I have left the newgroups....say it is me when it is she...The police officer told me that because its online and that its across states that she wont be able to do anything either as long as I have not threatened her or contacted her directly...everything I posted was also on my profile page...my account is closed now but I still worry she is going to harass me...so basically there is nothing I can do...even if I know who it is and have the print screens of her saying things? Because I supposed it would be hard to PROVE it was she using that screen name...although its clearly her pictures and her information??? And as long as she didnt use my name directly I would have to prove that she was saying them about me...even though they were clearly meant for me??? Im just so frustrated...she said she had a program that captured my ISP address and that I can run but not hide!!
Again there is very little that she can do to you or vice versa. Each person voluntarily avails themselves to the newsgroup. If they do not wish further communication, they may leave the newsgroup. If there is a problem with postings that violate the terms of service of the newsgroup, a complaint should be made to the web site host of that newsgroup so they make take action consistent with their internal company policies.
You cannot prevent a person from saying things about you to others on the internet any more than you can prevent a person from talking to people about you. If the statements made rise to the level of defamation, it may be actionable. Even then, however, in most cases, you must show tangible damages, which seems unlikely
If there is direct contact that it is unwanted, like a phone call, emails or text messages, or there is a threat of potential physical harm made, it may become a legal matter where you may seek a civil harassment restraining order or criminal charges.