How to survive the remaining 5 months of my postdoc in toxic environment?
Although I may not have stood in your shoes as a post doctoral scholar, however I hope I can give you some insight on the behavior of your PI.


  How do I survive the remaining 5 months of my postdoc with an abusive mentor who has unreasonably high standards?


First and foremost, don't take it personally.

If your PI is for lack of a better word an a**. I doubt there is anything you can do to change that. On the other hand, what you can control is your perception and acceptance of such negative behavior. 

Peeling back the emotional layers, is there truth to what is being said? Is there a fundamental misunderstanding on your part of a given subject matter? For example, if your PI berates you in public on not knowing that 1+1=2, you can approach the problem from two (among many) views. One is emotion: your PI just humiliated you in front of your peers. The other is the core issue at hand, knowledge, does 1+1 really equal 2?

With emotion: you can perceive it with the desired emotion or you can dust it off with nonchalance. Reply stoically "I didn't know that, thank you for pointing it out to me". Address the outburst and move on.

If you don't let hate (and in this case, a severe lack of tact on part of your PI) get to you, it robs the abuser of their satisfaction (if it was intentional). If it wasn't intentional, then it is a rather rocky learning process for your PI as one day, when their supervisor (or senior faculty) sees this going on, they will get their a** chewed out for humiliating their people or find themselves without anyone who is willing to work it them, effectively being an academic pariah. (Yeah he/she is smart, but he/she is a pain to work with, let's not).

With knowledge: it will be up to you to determine if you are in fact, in the wrong. If so, adapt your understanding with newfound knowledge and move on. If you are wrong, you are wrong, there isn't much more to discuss. If you are right... well... ask yourself if it is worth the battle to prove to a belligerent PI that they are incorrect. 


  I have been so stressed since the past month that I feel unfit for any position. How do I regain my confidence?


Take a moment and look at all of the struggles that you've accomplished and overcome thus far. Your graduate tests, qualification exams, writing a dissertation, defending you thesis, buying your review board's favorite foods, for the last >4 years of your life. Putting up with an a**hole for the next 5 months in comparison is a drop in the bucket.

Keep your eyes forward on the goals you've set for yourself and what kept you going all these years.


  How do I find a position without a reference letter from the current adviser?


My understanding of a reference letter, is to have someone who is knowledgeable of your work ethic, vouch for you. I believe there would be more than your PI whom you've worked closely with this past year. A faculty member perhaps?