It was very fun to stare slack-jawed at a screen for 45 minutes trying to understand what was happening, and I did manage to largely follow the plot, but seeing as how I'm a new audience to this insanity, can anyone just throw in some production context? Like why or how was this made, was it based on a manga, who made it and do they produce similar things or was this an example of how far you could stretch a dollar to make a crazy story?
The same director went on to direct Tengen Toppa Gurren Lagann, Kill la Kill, and Promare. None of them are as wild as Dead Leaves, but all are top tier anime. He's one of my favourite directors, and knows how to balance comedy, action and art perfectly.
You forgot to mention Panty & Stocking, Inferno Cop and Space Patrol Luluco. Luluco should be watched only after Kill la Kill and Inferno Cop (and the short Sex & Violence with Machspeed, can be found on Youtube).
Hiroyuki Imaishi is the greatest anime director out there.