A kook is someone who writes or produces articles and materials that seem completely detached from reality. The kook has had a vision of the world that's different from yours or mine, so different and so compelling that he feels he must tell the world about it, loudly and repeatedly, often with the implication that if he doesn't get his message across we're all somehow doomed. The canonical kook website is Time Cube, but Demon Busters comes a close second. As you might guess from the examples, kookiness and excessive religiosity go together like sodium and water, but "science is wrong and I have it right" and "I know about an evil conspiracy to kill us all" are popular themes as well.
Designing a kook website is easy for the kook, but for the professional designer, hitting that hysterical high just right is damned near impossible. Compared to grungy or minimalist design, kook design is a genre better left to the kook.
I'm going to send you to two websites that, I think, show this quite nicely. One or the other will probably offend you, and neither is safe for work. The first is America Forever, an earnest anti-homosexuality website out of Utah that encapsulates much of the kook aesthetic.
The other is The Landover Baptist Church. Landover Baptist tries to look like a kooky site, but LB is a parody of kooky websites and, unfortunately, it fails in the most important feature of a kook website: it's too well-organized.
A kook website has one premise: the message is so important, so compellingly obvious and so obviously compelling, that things like "design" and "aesthetic" are wasted efforts. For America Forever, throw in the American flag for a background, an animated mailbox for the contact info, use poorly dithered gifs, color text-filled graphical links with the only filter you know how to use on your pirated copy of Photoshop, don't use titles or alt text ever, and a single panel layout for the entire website. A kook website uses new text colors whenever the writer has a new thought, and often emphasizes ideas through seemingly random capitalization.
Even better, be incoherent while dedicating thousands of words to your obvious and compelling message. America Forever embodies a single, simple, ridiculous conceit: if sodomy is decriminalized, so many people will find sodomy so compelling that not enough people will have the kind of sex that makes babies and therefore the human race will die off. Here's how she words it (and note the capitalization of "anti-species" there, a perfect kookism):
The simple suggestion of homosexuality and lesbianism (gay) should be criminal when exposed to children because it forces the adults to explain same sex union, which is an Anti-species concept to minors, meaning that the basic argument for this attraction is pleasure. With it, comes an illogical explanation of using other members of the body, that do not identify sex, to replace the organs of the opposite sex, with the attempt of reaching sexual pleasure.
America Forever is not a joke. The author means every word. On the other hand, Landover Baptist is a joke, the longest-running website parodying far-right fundamentalist Christian thought on the Internet. With a tagline like "Where the Worthwhile Worship, Unsaved Unwelcome," and regular features like "Betty Bowers Is A Better Christian That You," Landover skewers excessive religious earnestness with an earnest tounge firmly planted in its cheeks.
Landover Baptist tries to be kooky: it uses red and blue, but the cream-colored background blows the frothy Americana look. The text is clean and readable, written and edited by someone with a firm grip on the English language, someone clearly interested in getting the joke across. It has a unified color scheme, a dead giveaway that the writer is not a kook. Its worst crime, however, is the consistent use of a grid layout. It's too clean. Too much time has been spent providing margins and padding. Everything is marked in ten-pixel increments, the images are well-formed (but, sadly, not Section 508 compliant), and the use of borders and rules sets important items off and apart from one another. It'll never win any awards, but it's a fully usable website that fails the kook test by shying away from being so kooky as to be unusable.
Designing for the kook ought to be easy. It looks easy. But hitting the mark is harder than it looks.