Would Jesus of Nazareth have known about Socrates or Plato? Philosophical schools?

He would certainly not have been educated in Greek philosophy. He didn't read or speak Greek and was not from a class that would have had access to libraries, and isn't known to have frequented large urban Hellenized centers like Alexandria or Caesarea. I suppose he could have picked something up by word of mouth, but if his teaching process as recorded in the Bible has any truth to it (and that is another question) it doesn't look like he adopted the Socratic method. Socrates almost always just asks questions (whether we're talking about the historical Socrates or the literary character Socrates is also another question). I can't think of a single question Jesus asked in a lecturing context. Admittedly it's been a while since I systematically went through the gospels. I am not in a sleeping mood so I'll have a look now.

Ok, a brief scan of my red letter NIV shows Jesus asking rhetorical questions, not like Socrates' apparently honest questions, so the teaching method is entirely different. An example Matt 11 7-10

What did you go out into the desert to see? A reed swayed by the wind? If not, what did you go out to see? a man dressed in fine clothes? No, those who wear fine clothes are in kings' palaces. Then what did you go out to see? a Prophet? yes, I tell you, and more than a prophet. This is the one about whom it is written: "I will send my messenger ahead of you who will prepare your way before you."

Jesus' method of teaching was to point out what text should inform someone in a particular circumstance. Socrates' method was to question all convention. They both sometimes used metaphor and analogy, but I don't think that's good evidence that Jesus had any deep knowledge of Socrates' methods or ideas. Jesus relies heavily on "what is written" while Socrates mostly (but not always) thought writing was corrupting society.

So no. I don't think Jesus had the language to learn from Socrates, I don't think he had the social position to access Plato's texts, and I don't think his teaching practice reflects the Socratic method.

That's not to say I think Jesus was a bad teacher. Socrates was kinda an ass and I probably would have voted to kill him too if I were on that jury. Socrates was a guy who didn't have solutions, only challenged institutions. Jesus, whatever you think of him religiously, was at least trying to be constructive.