Characters who are eccentric, nutty or mentally unhinged tend to demonstrate this in everything - including language. They often invent their own words or use the existing ones in strange ways, employ peculiar syntax and grammar. From time to time, they may also use a Perfectly Cromulent Word.
Compare with Buffy Speak.
- Hinata from Haikyuu!! has a habit of describing things with sound effects, especially when he's excited. Other players occasionally do the same, such as Kageyama, Nishinoya when explaining receives, or Nekoma's Inuoka (leading to an excited and perfectly incomprehensible conversation between him and Hinata that consists almost solely of sound effects).
- Mizuki from DAYS is also highly prone to explaining things using sound effects and, in fact, incapable of issuing or understanding normal explanations. He also includes words from foreign languages into his speech sometimes, usually thinking they mean something other than they actually mean.
- Hay Lin from W.I.T.C.H. tends to use the words "spacious" and "cosmic" as synonyms for "cool", and also sometimes invents her own words like "weirdific" and "rockalicious".
- Delirium in The Sandman tends to do this occasionally-which makes sense, since she's basically the personification of being a Cloudcuckoolander.
- Ensemble Stars! is filled with Cloud Cuckoo Landers, and also features a lot of characters with strange speaking styles in one way or another:
- The best example is probably Kanata, who speaks entirely in hiragana, uses a tilde ~ at the end of most sentences, and uses a lot of onomatopoeia, most notably 'puka puka' (meaning roughly 'bubble bubble'). Altogether, it portrays a relaxed, childish speaking style.
- Natsume's speech is even weirder - occasionally he'll speak in an entirely different font, which is referred to as 'magic language', and which is almost invariably Brutal Honesty. He also usually speaks the last syllable of each sentence with katakana, though what this means is not at all clear.
- Leo also speaks in a very whimsical way, greeting people with 'uchuu!', which literally just means 'space'. (Though it sounds a bit similar to 'chu', which is the onomatopoeia for kissing, so it sounds much less strange in Japanese than English.)
- There are also a lot of characters which aren't as strange as the 5 Oddballs (and Leo, often noted to practically be one), but who do have very intense quirks that impact on their speaking styles - for example, Souma is such a Samurai fan that he speaks in an extremely old-fashioned language, often using long-outdated sayings, and never uses the more modern katakana even when speaking loanwords, which implies a difficulty pronouncing non-Japanese words.
- Ever After High has Riddish / Riddle-ish. The rhyming language of the usually mad residents of Wonderland.
- In the Fate series, the Mental Pollution trait is explicitly described this way. Servants with the trait cannot be understood (or influenced) by anybody who does not relate perfectly to their disturbed worldview.
- Truth in Television actually. One of the common symptoms of schizophrenia is the tendency to invent neologisms.