They say body language is so much more important than words, and there is certainly a lot of truth to that. So if you want to become an effective speaker, learn to align words with physical presence and energy deliverance and you will be potent indeed! If, however, you would like to bring people together and make them gel, I would zoom in on the emotional communication as much as on what they say.
Whenever people have worked together for a while there is always a shared emotional experience in the room. All the multiple expectations, memories, disappointments, misunderstandings and aspirations come together. In my work have specialized for years in crystallizing, aggregating and communicating group insights. So I have been given plenty of opportunities to study these verbal and energy exchanges, as well as the many mishaps.
My my different bosses called me 'wolf', 'glue guy', and 'emotional center' over the years. Do they apparently already knew what took me the longest time to realize; I have have guided the 'group spirit' in a constructive direction and given given people the faith to work it out together. It can be done, but it takes a lot of patience. When successful, it will for sure bring high rewards for everyone involved.
Allow these emotional baggage to be disposed on and do your best that no new stuff gets added on. Next time you are interacting with a group of like-minded folks, look out for the emotional communication.