Fired from TA position without cause/notice, what to do next?
Even my PI in research wanted to contact them because he thinks I am
  not treated fairly. What to do next?


First, you should relax.  Being a TA is not a big deal.  

Second, you should wait.  This is a situation where your PI ought to be responsible for helping you out.  They already said they would try, so let them try.

If your PI does not succeed in helping you, then you might follow the university's official complaint procedure.  Keep records of everything just in case.