Hank Williams, Sr. faced the same kinds of difficulties the greasers face in The Outsiders. Williams died at 29 from alcohol and drug abuse.
At the end of The Outsiders, Ponyboy thinks about all the boys who die young because they do not know there is good in the world, and because they do not know how to get out of their rough lives. What do you think--was Hank Williams this kind of boy?
Not only could the Greasers relate to his music, they could relate to the personal demons he battled as well. As did the Greasers, Williams battled things that almost seemed out of his control. Even though the appearance was given in most circumstances that this was the life each individual chose, they were not happy lives.
I would say that the reason that the greasers could relate to him is because of how hard his life was. If you ever listen to (a number of) his songs, and if you ever read about his life, you will understand that he had things really tough just like they did.
For example, there is a Hank Williams Sr. song called "I'm So Lonesome I Could Cry." I can totally see a lot of those guys relating to that song. Maybe not the Curtis brothers because at least they have each other. But don't you think that Johnny would relate to that, or maybe Dally?
So, like many old time country singers, Hank Williams had (and sang about) a tough life with a lot of loneliness and betrayal. I think that the greasers can identify with those themes.