First in most of the examples you gave, it will be hard to prove that you did not do the things they saying, and if your company has not given you a warning, if your company has not fired you,or if you comany and not refused you a promotion, then you have no real "loss" to sue for.
Normally you will have to show some loss that can be measured in money to sue for.
Next I don't want to sound wrong, but this is about what every office in America is like, I worked in the corporate world and the people in various positions lied often, once I lost a job because of it, I left my breifcase on a desk while visiting a factory that my company was over. I guess either the janitor or the manager looked into it and saw my pay stub.
A few weeks latter when they did not like my report, they called my bosses saying I showed them my check and wanted more money if I was paid so much.
I never showed anyone anything, but they knew the figure, so I could not prove I did not show them, my word against thiers, no case that I could win in court. ( and I did try and ended up paying their legal fees when I lost)
Even in church "politics today" people call the church eldor and tells them did you hear what the pastor did today, or perhaps what I posted on one of these posts. Perhaps that I ate lunch with this person or that person.
By showing up the other girls, they have decided to get your fired, to make them look better, not right, but done every day in America business. You need to talk to the bosses about it and should have long before this.
But in the end, if getting rid of you, will make the business run better, they may even though it is the other three causeing the issues, but getting rid of one is easier than getting rid of three ( not right but what can happen