The girls in the Babysitters Club books often use outdated slang, as much of the series seems to be stuck in Ann Martin's own 1960s childhood. In one particularly cringe-worthy example, Claudia uses the phrase "What a hoot!" in a completely non-ironic manner. The girls also have a habit of inventing their own words to use in place of "cool," such as "dibble" to mean "incredible".
The band in The Last Days use the word "fawesome". Over. And Over. And Over. And Over. And Over. It's not clear if the author knows that that its an abbreviation of 'fuck awesome'.
Elinor M Brent-Dyer's Chalet School books from the '20s-'30s had American Chalet Girls using all kinds of weird and wonderful slang, such as 'rubber-necked four-flusher', 'glumph' and 'splay-footed'.
In Fear and Loathing in Las Vegas, Raoul Duke picks up some of the literature available at the anti-drug conference and flips through it. He notes that none of what is described as "drug culture slang" is correct, specifically noting the use of the word "tea shades" for sunglasses.
In Harry Turtledove's Timeline-191 series, the majority of which is set between 1914 and 1945, we get an early 20th century version that could be considered a subtle parody: numerous characters comment on the word "swell" replacing "bully," and their difficulty adjusting. Turtledove is also fond of using the phrase "lick 'em" (It basically means "we'll kick their ass!"). It shows up in just about every time period his books are set in: 1880s, 1910s, 1940s, 2080s...
In the Legends of Dune prequels there are things called 'Cymeks,' apparently trying to combine 'cyborg' and 'mech' with a Really Kool K. Cybernetic and mechanical, huh?
Probably the oldest example here, P. G. Wodehouse used a lot of slang from the 1890s in his works. Probably intentionally. While a keen observer of human nature, playing with language was Wodehouse's priority and he tended to write characters as rather broad archetypes or even stereotypes. The anachronisms serve as a shorthand for each character type and tend not to detract from the overall sparkling dialogue. An example is his American characters, who are constantly, clumsily, forcing words like "gee" and "okay" into their speech.
The series Percy Jackson and the Olympians slips into this at times, but it's not too bad. You just see the occasional overuse of "totally", "dude", and the modern "tween" protagonists talking about how they're going to "whoop some monster butt". And it gets much better as the series progresses.
In the column "Dude, Read All About It," Dave Barry explains how newspapers have been trying to attract younger readers to boost their declining readership:
If you read your newspaper carefully, you'll notice that you're seeing fewer stories with uninviting, incomprehensible, newspaper-ese headlines like PANEL NIXES TRADE PACT, and more punchy, "with-it" headlines designed to appeal to today's young people, like PANEL NIXES TRADE PACT, DUDE.
Subverted in Garth Nix's Keys to the Kingdom, when the characters seem to use offbeat slang. If the reader pays attention, they realize the series is actually Twenty Minutes into the Future, and it's not confirmed that the characters are even speaking English.
E. E. “Doc” Smith's Lensman series is set at some point in the indeterminate future in which interstellar travel and communication is a relatively casual matter. While "Doc" Smith essentially created the 'Space Opera' genre, his characters use slang based on 1920s United States constructions, such as a male addressing a female as "toots". Of course, even if the 20s slang were missing, the mores and culture present in the books would still make the books wholly dated. There's also a fair amount of constructed slang, such as the substitution "QX" for "OK," and the constant use of the word "jets" for... personal ability and competence or something like that. This is all parodied hilariously in Randall Garrett's short story "Backstage Lensmen" where the slang gets so thick that even the characters don't understand what they are talking about.
Much of the communication in the series is done telepathically using the Lenses, which can be used to talk to everything from humans to Starfish Aliens. The author's use of 1920s-era slang may be a translation convention, intended to represent to the reader the way that Kinnison's thoughts sound inside his own head. It still sounds really weird, and it contributes to the Zeerust atmosphere of the series.
The series usually steers clear of Totally Radical by just not having their characters use slang. For a period lasting 2 or 3 books, however, they tried to introduce "honkin'" as a slang term. It didn't stick.
A less ambiguous example would be when Cassie worried that her mother, who was supposed to make a speech in front of her class, would embarrass her by trying to namedrop bands like "Boyz Eleven Men, Snoopy Doggy Dog, and Nice Is Neat". Rachel manages to translate the first two, but needs Cassie to explain where the crap she got "Nice Is Neat"; it turns out that "Nice Is Neat" is how Cassie's been getting her mom to let her bring Nine Inch Nails albums into the house.
Invoked by one of the characters. One comments that they'd "bet dollars to donuts" on something and another comments "Something your grandmother used to say?"
Lampshaded in a Discworld footnote of a footnote describing the final test of the Monks of Cool:
"Yo* Cool, but not necessarily up to date., my son. Which of these is the most stylish thing to wear?" "Hey, whichever I select."
The novel Night Runner contains the line, "I'm the Master Chief and you just got powned."
Scott Turow's Innocent (sequel to Presumed Innocent) has the youngest character (28, compared to the main characters being in their 50s and 60s) talking in the most totally radical way, especially about how "completely tuned in" his girlfriend is.
Robert Bloch was rather prone to this in his short stories when he was sending up beats and hippies, making it more like Totally Hip, Daddy-O or Totally Groovy, Man.
Harry briefly talks like this to the Red King, since his words are being translated into the language the Red Court uses (presumably an ancient Mayan dialect) and he decided to annoy that translator by choosing words that would be difficult to give any kind of reasonable definition for in English let alone in a language dead for hundreds of years.
In a milder example, on one occasion he tells Michael "that's how I roll," much to Michael's amusement (given that by this point in the series Harry is pushing forty). Then it's lampshaded when Harry claims he heard Molly (Michael's daughter and Harry's apprentice) use it, so "it must be cool."
"A big ten-four to that, good buddy," said Tails. "We've gotta get hip and dig his crazy scene, find his pad, cash his chips and everything will be copacetic. It'll be very."
Bill O'Reilly's O'Reilly Factor For Kids is worse than it sounds. The lowest point is the periodical mock instant messaging sessions with the most outlandish acronyms. There is a handy little glossary in the back that explain to you what phrases such as "YYSSLIBTO" and "-6%" stand for ("Yeah yeah sure sure like I believe that one" and "Not very clever" respectively).
Neatly sidestepped by Anthony Buckridge in his "Jennings" series of school stories, by making up most of the schoolboys' slang, so it couldn't be "wrong" or dated.
Averted in A Clockwork Orange: author Anthony Burgess, a professional linguist, actually thoroughly studied contemporary teenage slang, but then decided not to use it as he wanted his story to be set in an undecided point in the somewhat near future. The result was a special slang he invented named ‘Nadsat’ (from Russian ‘-nadtsat'’, meaning ‘-teen’), which was English mixed with some rhyming slang, archaisms (intentionally using Ye Olde Butcherede Englishe), a few neologisms and borrowings, and lots and lots of Russian words (as it was The Cold War and Russian, which Burgess spoke, was very intimidating, hence suitable for gangsters).
Arguably the most horrifying thing about The Langoliers is the dialogue given to teenage girl Bethany Simms ("Totally tubular!").
In Rally Round the Flag, Boys!, Comfort Goodpasture speaks in what is described as "an execrable mishmash of teen-age patois." The narration sometimes imitates her habit of affixing "-sville" to adjectives and buzzwords.
A 2011 issue of National Geographic (which tends to be aimed at ages 18 and up) introduced a story about the "teenage brain" with "Like, totally!" Teenagers haven't seriously used that expression for about two decades now.
Diesel, a loner from Warrior Cats, is the most obvious character in the series to speak like this. Heck, he even keeps calling Graystripe "bro"! Occasionally in the later books, too, a young cat will say "totally" or call something "cool", which sticks out when compared to the fairly formal speech that the Clans mostly use.
All of James Patterson's young adult novels sufferfromthis. The second W&W book (The Gift) does this deliberately at one point - Whit likens the slangy talk of the guys asking about the illegal rock concert to camp counselors trying too hard to sound cool. It's these little details that make Whit suspect they are secretly NewOrder.
In Reconstructing Amelia the actual teenagers mostly avoid this in their dialog and texts, which sound just about right for the time period (late 2013), but a popular (and unauthorized by the school) gossip blog called gRaCeFULLY is full of this. It turns out to be a clue that the blog is run not by a student, but a teacher. And one character's avoiding this compared to the blog makes it significantly harder to tell they're actually an adult until The Reveal.