Fun topic, right here! My characters are fairly exaggerated in their styles, because I've incorporated elements into all of them that stand out physically, but also tie into their personality/character types/etc.
My character Gemini, went through radical design changes for years, because a few years ago, I came up with one comic story concept that I wanted to put a female lead in, but then I would drop the story for a new one, changing her design in each one until I landed on the story I wanted. My first story was paranormal, and I made her short-haired and tomboyish looking, with a baseball cap (I never really see females with ball caps) where she also had telepathy, and then my second story was going to take place with powerful warriors in space that defended their planets in teams, and the uniforms kind of looked like a cross between superheroes and American Gladiators-like outfit designs. Gemini remained similar looking, but in different attire (she even had her device, but it wasn't for absorbing enemies. They were mechanical dragon heads attached to chains from gauntlets on each one of her arms). I ditched that idea and burnt out on creating a new story for sometime, until I came to my current concept. When I did, I scrapped her design completely, only kept the name, and pretty much made the opposite of what she was.
I came up with the long pink pigtails as a polar opposite to the short black hair that I had before. I actually let my hand flow and improvise on the spot instead of thinking too much of what she should be like. Instead of a jacket, I did a vest and a corset. Instead of pants/shorts, I did a skirt/stockings. Instead of shoes, I gave her bloody hooker boots and had a good laugh with that (only when I started fleshing out her actual character, I did come up with a good, practical use for those platforms, which you'll see later). Late into her design, I used to even have these metal clasps around her pigtails to hold them in place, and then I switched them to black ribbons to compliment the rest of her colour scheme. Even the spade design on her represents the small group of female scientists she works with, called the Queens of Quantum. Each of the 4 members has a queen-of-a-card symbol design to them. And if you're wondering, how a chick dressed like this is a scientist? That's unbelievable. Well, my story is a little weird, but I do have reasons why she looks the way she does, acts the way she does, and has the career she does. But I just started my comic, so I'm not going to tell those reasons why before putting them into motion. All you need to know is that I actually do have reasons behind my designs and characters, as off-the-wall as they may seem. My wife also says that Gemini kind of looks Sailor Moon-ish, which is funny since I've never actually watched that anime. I don't really know if she borrows inspiration from any other character. I was honestly just going for broke, making her the opposite of the character type I had before.
Aside from Gemini, I spent months designing characters around simple, ridiculous concepts, and then I've surprisingly been developing them off of those ideas, with backstories and ways of speaking/interacting that really work. I've got a really diverse cast of characters now, from a cowboy ninja, to a gruff old sergeant that shoots rainbows, to a intentionally overpowered and super-psyched up DBZ-like swordsman, to a secret agent, to a scottish Santa Claus, to a dominatrix grim reaper, to even a man made out of beer (and many more). I like a good, lighthearted story with characters that reflect that mood, but I also like that I have the wiggle room to take these off-the-wall designed characters, and actually give them stories and ways of talking that are worth reading about.