It's not an anime, but the 2012 live-action film For Love's Sake is based off a manga from the 70s. It's a Japanese version of Romeo & Juliet crossed with High School Musical featuring amazingly corny dialogue, weirdly stilted choreography, and songs that don't make a lick of sense. Having said that, it's absolutely the most entertaining film I've seen all year. Mostly because of how seemingly 'bad' it is; in many ways, the film becomes ridiculously charming as a result. I can't remember any of the songs for it, but I'll definitely be first in line if it gets released again in cinemas or comes out on DVD. It's the definition of a cult movie waiting to happen.