What is George's birthday in Of Mice and Men?

This is a good question, but the fact is that there is nothing in the story that tells us George's birthday.  In fact, the birthday of no one is mentioned or celebrated.  This point is significant. 

When it comes to George and Lennie, or other migrant workers, they have very little.  So, within this world, there is no talk of birthdays. In fact, people are so closed to each other and alienated, no one experiences...

This is a good question, but the fact is that there is nothing in the story that tells us George's birthday.  In fact, the birthday of no one is mentioned or celebrated.  This point is significant. 

When it comes to George and Lennie, or other migrant workers, they have very little.  So, within this world, there is no talk of birthdays. In fact, people are so closed to each other and alienated, no one experiences community.  Lennie and George are the sole exceptions.  The reason for this is that the men live in a adverse environment, and so their goal is just to survive, which is no easy task. 

The only information that we have about George and his birth is that he, like Lennie, were born in Auburn.  Here is the text:

"Him and me was both born in Auburn. I knowed his Aunt Clara. She took him when he was a baby and raised him up. When his Aunt Clara died, Lennie just come along with me out workin’. Got kinda used to each other after a little while.”