Classical statues are also Japanese idols! Well, almost. They're not even head-to-toe statues. They're just busts, mostly stopping at the pectorals. Don't hold me to this, but I think they're Donatello's St George (1415-17), Michelangelo's Giuliano De Medici (1526-34), Hermes (taken from the ancient Greek sculpture of Hermes and the Infant Dionysus) and Mars (taken from the Ares Borghese that's currently in the Louvre).
They really are just statues. They can't move. They don't even have legs. Their manager (Miki Ishimoto) has to lift them on an airport luggage cart to take them to the car to do their gigs. However they can talk (how?), sing (okay) and even possibly eat (less sure about that). They talk like the airheads in a Japanese boy band, because that's what they are. They do concerts and appear on TV variety shows. This is basically just a boy band comedy with a surreal twist, although admittedly it's a pretty massive one. I liked it. If you're looking for absurdity, try this. It's reasonably funny, but it's the kind of silly that would have probably got old fast if these hadn't been just eight-minute episodes.
Medici seems like the youngest of them, which is saying a lot given how infantile they're all capable of being. (Ep.8, for instance, has them thinking the most important thing is to show up in a stretch limo and deciding that they're so amazing that they don't need to rehearse for a live TV performance. See also their bitchiness in ep.7.) St George tells jokes so bad that he becomes famous for them and his name becomes a new word. Hermes is running a fraudulent business to scam money off suckers in ep.5, although of course Ishimoto goes ballistic.
The show's mostly just running with the absurdity and having fun with it. The last few episodes have more of a story, but even there it's all still basically for comedy. Ishimoto and the Medici warehouse in ep.12 made me laugh, for instance. It's silly. That's the whole point. I laughed at the enka singer in ep.2 and at pretty much anything that expanded the gag of Greek gods and/or sculptures living in modern Japanese society. Is there anything more to discuss? Nope. The boys are silly, but their career is a perfectly normal one for a modern boy band and Ishimoto's certainly taking her job seriously. This show is almost exactly what you'd expect of an anime where the lead characters are classical statues in a boy band.