Would Jesus have been educated or familiar with the teachings of Plato, Socrates, and Aristotle? What do we know about the education of young Jews of his time period?

So the simple answer to this would be: probably not. The longer answer is, in order for Jesus to have studied these philosophers, even on a basic level, he would have had to have learned how to speak, read, and write ancient Greek, and while there is a legitimate chance he could have spoken greek, he likely didn't learn to read and write it. However, at the heart of this question is asking what Jesus' educational level, which Bart Ehrman addressed in his book, Jesus: Apocalyptic Prophet of the New Millennium where he says:

There are multiply attested traditions that Jesus spoke Aramaic. Sometimes, for example, the Gospels quote his words directly without translating them into Greek (see Mark 5:41; 7:34; John 1:42). This would make sense contextually, since Aramaic was the normal spoken language of Jews in Palestine in the first century. Moreover, there would be no reason for anyone to make up the tradition... It is also indicated in the Gospels that Jesus could read the Scriptures in Hebrew (e.g., Luke 4:16–20; see also Mark 12:10, 26), and that he eventually became known as an interpreter of them. He is sometimes, for example, called “rabbi,” that is, “teacher” (see Mark 9:5; John 3:2). At the same time, there are independently attested traditions that those who knew about Jesus’ background were surprised by his learning (Mark 6:2; John 7:15).

Together, these data suggest that he did learn to read as a child—that is, that he had some modicum of education—but that he was not considered an intellectual superstar by the people who knew him as he was growing up. There are no traditions that specifically indicate that Jesus spoke Greek, although some historianshave surmised that living in Galilee, where Greek was widely known, he may have learned some. Moreover, some have suspected that he communicated with Pontius Pilate in Greek at his trial—although we will see later that it is very difficult to know exactly what happened then. At best we can say that it is at least possible that Jesus was trilingual—that he normally spoke Aramaic, that he could at least read the Hebrew Scriptures, and that he may have surmised that living in Galilee, where Greek was widely known, he may have learned some. Moreover, some have suspected that he communicated with Pontius Pilate in Greek at his trial—although we will see later that it is very difficult to know exactly what happened then. At best we can say that it is at least possible that Jesus was trilingual—that he normally spoke Aramaic, that he could at least read the Hebrew Scriptures, and that he may have been able to communicate a bit in Greek. The final point is, in my judgment, the least assured. (P. 99-100)

So we've established that he was likely literate in at least one language (which already made him elite since about 90% of the Roman occupied population during this time period was illiterate), but it was most likely primarily directed at learning and teaching about the Torah. Also, in all my studies of of the New Testament (and also classical Greece from my undergraduate degree) I've never seen anything to suggest that Jesus learned or incorporated these ideals into his teachings.

And to answer your final question, most Jews during this time period were illiterate. We know that at least two (probably most) of Jesus' followers were illiterate and uneducated as well. Next I'd like to pull in a quote from the bible, specifically the book of Acts, where it talks about two of Jesus' most important followers.

When they saw the courage of Peter and John and realized that they were unschooled, ordinary men, they were astonished and they took note that these men had been with Jesus. (New International Version)

Now the word "unschooled" here in the majority of ancient manuscripts is: ἀγράμματοί (agrámmatoí). This word is often translated to "unschooled" or "uneducated" but typically it directly implies that they are illiterate. That said, it would then suggest that these men didn't know how to read or write, making it likely they were never taught anything of significance about Greek Philosophers.

It's also worth noting that philosophy wouldn't have generally mattered to peasants, especially for middle of no-where towns like Nazareth. These men and women of this time period were preoccupied with following Mosaic Law and following it's teachings, so learning about other philosophies could have been sacrilegious during this time period.