What you are getting at is wanting to sue or press charges against your employer for lying about the reason for your termination to the unemployment system, right? My question to you is how far has this gone? Have you been denied benefits initially? Have you had an appeals hearing, and then been denied a second time?
When you are discharged and file a claim, EDD will investigate the situation, regardless of the reason you say you were terminated, and regardless of the reason the employer says you were terminated. It would be to your advantage if you get to draw benefits. It would be to their benefit if you don't. There is the assumption, in this agency investigation, that ONE OR BOTH of the parties involved may be lying. The more definitive the proofs that either party can provide that it happened as they say it did, the more they are likely to prevail in the decision, being considered the "more believable" of the two parties. That is who they go with, the more believable of the involved. The decision could be made, the adjudicator could get confirmation by either party showing documents, or it could be the testimony of others involved, or it could just be what you say versus what the employer says without additional documentation. This is an agency investigation, not a criminal investigation.
Whether or not you received warnings or write ups, if they believe you were really doing what they say you were doing, in other words, the multiple accusations of sexual harassment they mention, the unemployment system can say that you are guilty of "gross misconduct" which means you didn't have to have warnings or write ups, you should've known that you shouldn't be doing this whatever it was you were accused of even one time, and they had a valid misconduct reason to fire you.
In other words, they may be lying their heads off, every one of them, but if they're more believable than your story, they prevail and you get no benefits. And there's no recourse except the standard number of appeals.