In the early Silver Age, Snapper Carr was essentially the Justice League of America's collective sidekick. He spoke in constant slang and was always fixing hot rods, going to baseball games, and so on. Acknowledged in the JLA/AvengersCrossover when Marvel's Rick Jones says that Carr is an okay guy "no matter how he talks". And when Rick Jones thinks your slang is outdated, brother, you got problems.
Speaking of Rick Jones, there's a What If? issue where Rick Jones becomes the Hulk instead of Bruce Banner. This youthful Hulk mixes Hulk Speak with the early 60s version of this trope to hilarious effect:
"Don't jive Hulk with fancy lingo, bug-man! Hulk doesn't dig it!"
Bob Haney's work on the original Teen Titans comics of the mid-to-late 1960s could be the archetype of this trope. The least subtle display takes place within one such issue, which features Robin deducing that a message from an adolescent is a forgery based on its "vernacular". Daddy-O.
An issue of Deadpool spoofed this when the title character time travels back to the 1960s and encounters the then-current versions of Spider-Man's cast. Their constant overuse of inexplicable 60s slang is a running gag throughout the issue, with Mary Jane being the worst offender. And upon hearing Harry Osborn speak, Deadpool actually asks if he is having a stroke. This isn't the only time Deadpool's travelled back in Marvel history and made fun of slang. Brian Posehn's run has featured an 80's issue with alcoholic Tony Stark & a 70's issue (complete with afro-wearing Deadpool) trying to join Heroes For Hire and fighting an albino pimp called "White Man". As one would imagine, there's PLENTY to make fun of.
An issue of Superboy addresses this when the titular character seeks to reinvent himself after being given the cold shoulder by a girl for his over-use of early-90's cliches and expressions. However, all this accomplishes is trading sunglasses for bug-eyes (which were never seen again), a leather jacket for a PVC one, losing the piercings for a scruffy goatee, ditching his belts all together, and saying "Word. Reprezent." instead of "Don't Mess with the S!"
In Nextwave, Boom Boom uses phrases like "Oh noes!" and "ZOMG!" in both everyday conversation and periods of extreme stress. However, this is due to her actually being completely brainless, in the most literal sense of the word. Warren Ellis, the comic's writer, practically lives on the Internet and was taking the opportunity to lambast some of its stupider members.
The acid overdose survivor Arkady in Freakangels apparently starts talking in lolcat when drunk. "I can has vodka" indeed.
DC Comics's miniseries The Weird from the late eighties had the "son" of its eponymous character speak in terribly inaccurate slang — flying with his pseudo-father is apparently "bogus" and The Weird's abilities are "the dudest". Jim Starlin: good writer, terrible slangologist.
The front cover of DC'sRaven miniseries proudly states, "Finally in Her Own Emo Series!". Someone at DC is apparently unaware that emo, when applied to a person, is generally considered an insult.
Fray's anning hab of abrevving half of the words in every sent she speaks has a sim eff to the more comm vers of this tro on a lot of peep; that is, making it both hard to under and frustringly diff to igno. Lampshaded in Buffy Season 8 story arc The Time of Your Life, where Buffy is thrust forward in time and actually meets Fray. Upon hearing Fray speak, Buffy's response is, "Uh....English?" Later, after hearing more of Mel's Future Slang and such, Buffy makes a comment amounting to "I should have been kinder to the English language when I had the chance"
Archie Comics is notorious for this trope. For example, one late-80s story has a lifeguard tell a surfing Veronica, "I really dig the way you attacked those waves with your rad moves". A contemporary in-house ad for an Archie calendar features a cartoon teenager, sporting a ridiculous multi-colored mohawk, oversized shades that Elton John would reject, and mismatched-color clothes telling the reader, "I ordered mine!" Like gnarly, daddy-o, if a rad hepcat teen like him bought one, I better slap down the bread too, yo yo yo.
Archie Sonic The Hedgehog, despite advertising itself as "The world's most way past cool comic!", isn't actually terrible about this when it comes to its title character. Vector, on the other hand, sounds like he's having a stroke in a good half of the panels he's in. This was eventually toned down, then hand-waved as his initial attempt to hide his Downunda accent.
During the 80s crossover series Secret Wars, most of the cast is notoriously guilty of this. In particular, She-Hulk, when punching the Enchantress, declares "Oh wow! That was, like tubular, you know — TO THE MAX!" This example is even more absurd when considering the fact that She-Hulk is a high-end attorney.
2000 AD'sD.R. & Quinch written by Alan Moore has the title characters describe literally everything as "totally amazing," "unbelievably awesome," or, like, "incredibly stupid."
Subverted by Journey into Mystery (which used to be The Mighty Thor), where Kid-Loki has gotten his hands on a Stark-Pad and is casually surfing the internet. One hopes he won't go Totally Radical on us, and then not only does he use the same formal grammar as any Asgardian while typing, but he explains what he has discovered on the internet in equally archaic terms, making for great one-liners:
Loki: The humans of the Internet are uncouth!
Loki: I've primarily discovered that mortals like to rut and chronicle the experience pictorially.
Later in Young Avengers, Kid Loki displays some shades of the trope because he tries to fit in with a bunch of Midgardian children and also body snatching, so technically he isn't Kid or even a kid anymore. He loses it when he gets an age-up, though... and replaces it with occasional Buffy Speak.