I think I first heard of/saw this group on Salaryman's blog (he would feature a band like this). The three women form あやまんJapan (Ayaman Japan), and they sing silly, kind of dirty songs.
Apparently they started off as a group of party organizers, made an appearance on Fuji TV, and then broke into the music scene. It looks like they only got started musically (professionally at least) in 2010, so they've only released a handful of songs.
Yoshie's father hates them and she thinks they're kind of annoying, but I choose to be amused by them. Sure, they're not producing the highest level of art here, but their songs are kind of fun and different, if not catchy. And at least they're not another cute, innocent, generic J-pop group.
Here are two videos of what I believe is their original breakout song, 「ぽいぽいぽいぽぽいぽぴー」("Poi Poi Poi Popoi Poi Popi"):
Here are the lyrics with an approximate translation. As you can see, mostly a mix of nonsense and sexual references; basically just making fun of pop songs.
Here's one of their later songs, which starts off more subtly but then gets quite kooky (and for those of you who know what AKB48 are, yes, I think they are making fun of them):
Update: AKB48 is a large, ever-changing girls pop group (pictured below). I have a lot of problems with AKB48, but that's a story for another post. Below are a picture and video for reference, so you can compare with the more Ayaman Japan parodic video above.
Update 2: This one is much more blatantly making fun of AKB (it seems this post has taken a turn in that direction):