How does social justice relate to the plot?

The most obvious social justice issue in The Outsiders is the socioeconomic inequality, which is pervasive throughout the book. The Greasers encompass the poor and working-class population, while the Socs encompass the upper-middle and upper classes. The Socs and the Greasers hate each other. The Greasers envy the Socs, though they often frame their hatred in a way that labels the Greasers as superior. The Socs look down on the Greasers because of their relative poverty.
The socioeconomic differences bring other social justice issues into focus. The Greasers and Socs each have a territory in which the majority of their members live, and it is generally recognized that neither group should violate the territory of the other. The reason these territories exist is because neighborhoods have become largely homogeneous, with members of the Socs's economic class separating themselves from the members of lower economic classes. This separation can breed animosity. Importantly, the greater monetary resources of the Socs allows them to violate the territory of the Greasers without having to tolerate territorial violations by the Greasers, because the Socs have greater access to cars. This sets up a dynamic in which the Socs can use their access to wealth to ignore the unwritten rules followed by others, which also engenders greater animosity towards them from the Greasers.
The socioeconomic differences are also apparent in Ponyboy's home. His parents died in a car accident, leaving Darry to take care of Ponyboy and Sodapop. If the family had been wealthier, then Darry may have been able to attend a community college, or another family member with an established household may have been able to help with Ponyboy and Sodapop. Instead, Darry has to largely give up on his desire for college, despite his academic abilities, and work a lower wage job that will allow him to support his brothers. This prevents him from obtaining a college degree which may have allowed him to work for higher wages and move up to a higher economic class. The lack of resources and options for keeping the family together prevent economic mobility for Ponyboy's family.
There is also a criminal justice issue in the treatment of Johnny. While Johnny does kill one of the Socs, he does so because he and Ponyboy are being threatened. When Johnny stabs the Soc, Ponyboy is in the process of being drowned. This would be a clear cut example of the doctrine of defense of others, which allows an individual to use proportionate force to defend the life and/or safety of another. When there is a reasonable fear of death, an individual may use deadly force to defend another. Instead of recognizing that Johnny was acting to defend Ponyboy's life and his own physical safety, the District Attorney charges Johnny with manslaughter. It is highly unlikely that Johnny would have been charged if he were a Soc, especially because he would have access to a high-quality defense attorney.
While the difference between wealth and poverty is the up front social issue in The Outsiders, it also informs these other issues surrounding criminal justice, family care, social mobility, social diversity, and even security in property. It also demonstrates that social class can have a determinant quality upon one's life, even when merit would dictate otherwise.

Generally plot focuses on events. Things like rising actions, climax, and falling actions are plot related. Something like social justice would more closely associate with theme discussions. That doesn't mean social justice doesn't apply at all to the plot. If the question is looking for any relationship, then I think a case can be made that the social injustices found between the gangs does drive the plot forward a bit. The Greasers and Socs are on opposite sides of a socioeconomic divide, and they hate each other for it. The Greasers hate the entitlement and privilege of the Socs, and the Socs see the Greasers as nothing more than degenerate hoods. If this animosity didn't exist, Johnny never would have been jumped and beaten to within an inch of his life. He wouldn't be as defensive as he is either. When he and Ponyboy get attacked by the fountain, Johnny responds with quick and final violence. This forces them to the church and that entire rising action sequence. None of that would have happened if the members of both gangs had been given the same opportunities.