The Merriam-Webster Dictionary defines "reeling" as an adjective that means "having a feeling of being whirled about and in danger of falling down." For example, "the blood donor experienced a reeling sensation after standing up too quickly." Synonyms include aswoon, giddy, light-headed, swimmy, vertiginous, whirling, and woozy. Some related words are faint, weak, addled, befuddled, confused, dazed, and groggy.
The Merriam-Webster Dictionary defines "pickled" as a slang term that means "being under the influence of alcohol." For example, "I must have been rather pickled when I agreed to your stupid scheme." Synonyms include besotted, blasted, blitzed, blotto, bombed, boozy, canned, cockeyed, crocked, drunken, fried, gassed, hammered, high, impaired, inebriate, inebriated, intoxicated, juiced, lit, lit up, loaded, looped, oiled, pie-eyed, plastered, potted, tipped, sloshed, smashed, sottish, soused, sozzled, squiffed, stewed, stiff, stinking, stoned, tanked, tiddly, tipsy, wasted, wet, and wiped out. These are mostly slang words. Some related words are maudlin, beery, befuddled, bleary-eyed, crapulous, dopey, rocky, strung out, stupefied, debauched, dissipated, dissolute, alcoholic, bibulous, and dipsomaniacal.
When put together, they create an imagery of people who have drunk a great amount of alcohol, so much so that they smell strongly of it and are also stumbling over and moving around in a manner that indicates inebriation. When Ponyboy makes the observation that the Socs were "reeling pickled," he means that they were very clearly drunk and exhibiting evidence of drunkenness.
S.E. Hinton's The Outsiders is a book that is full of slang terms from America in 1965, where the story takes place. The colloquialisms of Ponyboy Curtis's first-person narration lends to the very specific tone and style of the book. The main conflict and theme of the story revolves around two groups of teenagers who are divided by socioeconomic class. The use of slang, such as "reeling pickled" emphasizes the youth culture of the novel, as well as the two different "cultures" inherent in upper and lower economic classes. The strong language gives the narration a kind of story truth, meaning that the narrative seems much more realistic and in-the-moment because of the language.
At the end of the novel, it is revealed that the entire narration is from Ponyboy's English class assignment. He is writing about the recent tragic events in his life, and how he feels about them and how he has come to terms with them. The slang and casual language of the entire book makes more sense in that context. It is easy for the reader to believe that this is Ponyboy's essay for school, because the language is so realistic and expected from someone like him.
Notably, the depiction of underage drinking and the use of slang (both very realistic) have caused The Outsiders to be banned in some schools in America.