If various people have posted demeaning comments about me on Facebook can I sue them for slander?

No, but you might be able to sue them for libel. There are three requirements:
1) that the statements be false
2) that those making the statements knew they were false yet posted them with malice
3) that you were significantly and materially harmed by the statements.

All of these requirements pertain to this situation. Those making the comments knowingly posted false comments. They were all posted with malice towards me. And, the have cause me to have severe after effects including depression and anxiety.

Then consult an attorney.

... And, the have cause me to have severe after effects including depression and anxiety.

Normally, damages in defamation cases would involve people thinking less of you, not your own self-view. But maybe.

Let me add, that the only thing easily provable here is the veracity of the statements. It will be up to the defendant to prove that the statements were true. But it will be a lot harder to show they knew they were false and whether they acted maliciously.

As for your suffering from depression and anxiety. I'm afraid a court and especially a jury, is going to use a sticks and stones approach here. Why you would go into such severe depression over lies told about you on the Net will be a question.

I suggest you do some research on cyberbullying. There has been some recent cases of young people committing suicide over things posted about them on social media sites. You may be able to gauge the possibilities of legal action from the results of those cases.

But, if you think you have a cause of action, consult an attorney.

If various people have posted demeaning comments about me on Facebook can I sue them for slander?Hello J:

Nahhh... Damages are measurable MONETARY damages - not feelings. I don't think you have any.

excon