I would like to clarify and state that the tone of The Outsiders is not always ominous. It is at times, but not always. Most of the time, the tone is realistic. It's more akin to a news reporter reporting on a story. Hinton doesn't shy away from describing the graphic nature of gang violence and the toll is takes on these young boys. Of course her tone is a bit lopsided, too. She is definitely more sympathetic toward the Greasers. If Hinton's tone were entirely neutral, she would focus equal amounts of time on the Socs.
Hinton's tone switches to ominous when she foreshadows, and when she uses flashbacks. Here's an example of foreshadowing that makes use of the ominous tone.
"Things gotta get better, I figured. They couldn't get worse. I was wrong."
The quote is the last line of chapter three. Ponyboy is dropping a bomb on the reader by saying that he was wrong about things not getting worse. Stuff isn't exactly going great, but Pony's comment ensures the reader that things will get worse without giving specifics. That's ominous.
The ominous flashback is in chapter two. Ponyboy is explaining to Cherry what happened to Johnny to make him so skittish. The past tense and vague details lend an ominous tone to the retelling of events.
"We were passing it, kicking rocks down the street and finishing our last bottle of Pepsi, when Steve noticed something lying on the ground. He picked it up. It was Johnny's blue-jeans jacket--- the only jacket he had."
The dash and the final detail about it being his only jacket also adds to the ominous tone. It causes the reader to really take notice of that detail and wonder why Johnny would be without his jacket. Something bad must have happened.