I can't quite distinguish them, because "communication" is always social? I guess 交际 is like my social skills and 沟通 is used with "dispute" but is that it and what about 交流？
I am sure all three terms can be found in dictionaries, but some of the definitions might overlap and cause new learners confusion, I think it is better to just list their main difference in my answer:
交流 = interact / exchange
交際 = socialize
溝通 = communicate
文化交流 (cultural exchange) ; 互相交流 ( interact with each other)
交際應酬 ( socialize and partying) ；與上流社會交際 (socialize with the upper class )
無法溝通 (unable to communicate); 以眼神溝通 ( communicate with looks in the eyes)
I like using linedict.com for this, you can find example sentences which help us 老外 see how words are used.
Click the radio button Examples and enter a word. You get examples with English translations.