We know that Jedi are taken away from their families when they are very young, but do they ever have any communication with their families when they are older? Do they ever even know who their families are?
I’m fine with canon or legends answers.
Yes, sort of.
In Disney Canon - the novel Heir to the Jedi, Luke comes across a Rodian who knows her uncle was a Jedi who was killed by his clonetroopers during the Clone Wars.
"A member of our clan was a Jedi Knight. He was my uncle in fact, and though his devotion to the Order usually kept him far from Rodia, I saw him a few times when I was young. Of course, he was here on Jedi business - and of course, the Jedi do not maintain their family ties - but I was told who he was and even had occassion to meet him once or twice"
She leads Luke to the dead Jedi's grave, of which she says she is now the only family member to still visit, and with Luke's help, retrieves the dead Jedi's lightsaber (which was buried with him, as the family did not know what else to do with it as nobody else was Force adept) and gifts Luke the weapon
As his dying wish, he requested that he be returned back to his family:
"Like your father, he was betrayed. He was shot by clone troopers.....he made it into his ship, recorded a brief message about what happened to him with his astromech, and gave it orders to bring him back here....the clan wiped its [the droid's] memory...scuttled his ship and built my uncle a small tomb out in the jungle."
-Heir to the Jedi: Star Wars, Chapter 2
Yes, some might even live with their families, e.g., Ki-Adi-Mundi in the comic Prelude to Rebellion. Before Episode I he lives on planet Cerea, advises Cerean government, etc. Later his daughter is kidnapped by Jabba the Hut... seems to be a very exciting familiy life. ;)
See the article at Wookieepedia for details: http://starwars.wikia.com/wiki/Star_Wars:_Republic:_Prelude_to_Rebellion