In The Outsiders by S. E. Hinton, who do the two boys go to for help? Why is it significant that they go to this person and not Darry? ...

Johnny and Pony went to Dally for help because Pony was fighting with Darry and because Dally had more experience being on the wrong side of the law.

Johnny and Ponyboy find themselves needing help because of a combination of unfortunate events.  They meet some nice girls at the movies that just happen to be Socs.  The Socs’ boyfriends do not appreciate their girls hanging out with greasers.  The two gangs are constantly at odds.  The girls leave with their boyfriends, but when they find Johnny and Pony in the park later, there is trouble.

Johnny and Pony were in the park because Pony came home late and got in a fight with his older brother Darry.  Darry hit him, and Pony ran.  He felt that Darry was too hard on him and did not really care about him.  Johnny was from an abusive home and basically didn’t mind staying away.

In the park, the Socs jump Pony and Johnny.  They are Bob and Randy, Cherry and Marcia’s boyfriends.  Bob nearly drowns Pony, and Johnny intervenes.  He kills Bob, and the boys run.  They feel that Dally is the best person to turn to, because Dally has been in trouble with the law enough to know what to do.

"We'll need money. And maybe a gun. And a plan."

Money. Maybe a gun? A plan. Where in the world would we get these things?

"Dally," Johnny said with finality. "Dally'll get us outs here."

I heaved a sigh. Why hadn't I thought of that? But I never thought of anything.

Dallas Winston could do anything. (Ch. 4)

Dally does help the boys.  He has them hide out in an abandoned church and later comes for them.  This is how all three of them end up getting injured in the church fire, when they try to save a group of kids on a trip.  Johnny is injured enough that he will eventually die, so the boys do not really need to worry about being on the run anymore.

This experience shows Pony that Darry really does care about him.  It is difficult for Darry, because he is the older brother and has to be the father figure.  Pony's trouble really worries him, and of course he is horrified that his little brother is injured, and that he played a part in it by driving him off.  Their relationship is stronger from this point on.