It sounds like you are literally “caught in the middle” between your boss and the employees you are responsible for in your group. How dreadful for you, but kudos to you for wanting to do what is correct and ethical for your employees and for all parties concerned.
I do not envy your position. But at least take comfort in knowing that your situation is not unique - in fact, I think that an idyllic atmosphere, without tension, competition and strife, may even be the exception and not the norm, based on the many questions I have received that are similar to yours.
The “Jewish” approach is to try and create an atmosphere of harmony in the workplace without any slander, gossip forbidden speech. Based on your description of the workplace “politics” I would say you have two possible plans of action.
The plan you choose depends on whether you feel you are in a position to approach your boss and try and implement some system of change to try and improve the conditions for your group.
If you feel you can approach him and that he will be open to listen (and not fire you!), then I suggest the following. Tell your group members that you will try to speak with the boss and stop the verbal abuse and embarrassment. Ask them if they would please refrain from gossip while you make your efforts, so that you will have a better chance at success, and that the gossip only harms the positive energy of the workplace – besides other possible negative effects gossiping may have on their own selves for speaking in a forbidden manner that has no benefit. Even if they feel they need to speak against him to vent their frustration, perhaps you can encourage them to try to not rise to the bait of revenge, and instead act in a more elevated and dignified manner and see how they feel.
On the other hand, if you do not feel that can approach your boss or help bring about any change for the better, I suggest that you explain this to your co-workers, and that you personally try not to be present if there is gossip or forbidden speech in the office.
And, whatever course you choose, I strongly suggest that you make it clear to your co-workers and to yourself that although you may not be successful in your “political” efforts to solve the problem, not to forget that there is a “Big Boss” who will hold each one accountable for his deeds and speech – and you personally believe that ultimately justice and reward will be served from Above.