Do you know The Powerpuff Girls? This anime looks a bit like that. Primary colours and bold, childish lines. Imagine something for children, but with inappropriate content. This show includes toilets eating people, vomiting, being covered in faeces, casual sex, pornography, guns, swords, ultra-violence, a possibly undead and/or retarded dog shagging an unconscious man's head, condoms, the ghosts of intelligent semen, roadkill, nudity, nasal sex, knickers being used as a parachute, dildos and other sex toys being used to kill zombies, bondage, sexual deviancy, gambling, brain injuries, God being a giant woman in her underwear (possibly), angels, devils, a tough-talking black priest with a huge afro and our heroines going on trial for the crime of being themselves.
Those heroines are Panty and Stocking, of course. Garterbelt is the afro priest. Panty is a foul-mouthed man-eater whose attitude to sex is "the more the merrier" (either serially or everyone at once) and she'll abandon her work to enjoy herself with any good-looking stud who happens to be passing. She doesn't realise that handing out copies of her home-made pornographic film might create a potential public relations problem. Her weapon is her knickers. When she drops them, they'll transform into a gun and she'll shoot people with them. Panty doesn't really care who she shoots, what they might have been doing at the time or whether or not they deserved shooting.
Stocking has slightly less of an attitude problem, which is to say that she's just very very rude and offensive. She's a goth who loves pigging out on sweets. She has much less sex than Panty, but we do know that she uses sex toys, is kinky and is capable of displaying truly deranged taste in men.
It's a Gainax show, like Neon Genesis Evangelion, FLCL, Gunbuster, Mahoromatic, Ebichu Minds the House, etc. Gainax are a bit notorious. This show will have contributed to that, although that's reminded me to go looking for Ebichu Minds the House. From what I hear, that's another ostensibly kiddie-targeted Gainax show with offensive sexual content, played for laughs. Panty and Stocking is definitely the more violent of the two, though.
Did I like it? Dunno. Sort of. It's a laugh and it's got a cool theme song, but I don't think I'll ever need to watch it again. It doesn't have a storyline, except in the last couple of episodes. It doesn't even have episode-length episodes, since each episode is split into at least two independent misadventures. Panty and Stocking behave badly. Sometimes it's funny. That's all there is to it, really. Technically our heroines are angels, sent from heaven to fight the ghosts that threaten humanity, but let's just say that they live in a city whose name is a pun on the Japanese word for "fallen angel". Admittedly they do usually kill a ghost by the end of each half-episode, but not before they've turned the air blue, committed casual ultra-violence and shown no interest in anything beyond their ideas of fun.
There are extreme stylistic shifts. Ghost-killing isn't done with animation, but instead with live-action footage of Gainax blowing something up. Panty and Stocking are normally drawn as if the show's aimed at four-year-olds, but every so often they'll switch to a more conventional anime look. (This is usually when they're removing their knickers and stockings to turn them into weapons.) Then there's "Vomiting Point" (ep.5b) that seems to be exaggerating the anime film Tekkonkinkreet and so looks grimy-ugly-creepy.
What's that? Why, yes. Since you ask, there is indeed a half-episode called "Vomiting Point". Others include "Excretion Without Honor and Humanity", "Death Race 2010", "High School Nudical", "...Of the Dead" and "The Stripping".
It is quite fun, though. It's offensive in a good way, which even managed to attract a female fanbase. Panty and Stocking are strong female characters in a way that isn't being equated with "idealised and perfect", since instead they're absolutely appalling people who are nonetheless fun, badass and not apologising for anything. The show's treatment of sex is refreshing, especially with Panty. (She's sexually aggressive and almost insanely promiscuous, but the show doesn't have a problem with this and indeed builds a feminist message around her in ep.13.)
This anime has one delicate, blushing maiden who believes in love before sex. His name's Brief. It also has a pair of satanic devil-sisters who show up halfway through to be our heroines' nemeses. This isn't an important show. It doesn't matter and there's no need to study it or think deeply about it. It really is just a 13-episode exercise in pushing the boundaries of taste. I don't know if I'd call it "good" in any long-lasting sense, but I think it achieved in spades what its creators set out to do and I'm sure everyone had a ball making it. (Apparently it was thought up at a Gainax company party when everyone was drunk.) It's comedic sociopathy. I'm not sure if it's broadcastable in the West. It has a really good English dub, apparently, which swears the roof off. (Swearing just isn't the same in Japanese, although our anti-heroines do their explosively vulgar best.) You can't say it's not memorable, anyway.