already D.A.F. and Die ärzte are mentioned...
kind of not hitting the terms you wanted, but "Die Goldenen Zitronen" are some kind of intellectual prototype german Punkband. highly political/social criticism combined with lyrical twists and turns.
edit:
"Ton Steine Scherben"
!!!
How could I forget?
they cover almost anything you have mentioned, including gay love hymns everybody knows in germany. they started pretty trashy/extreme and kinda started to know their instruments better. Rio Reiser was their frontman, he also started a pretty succesful solo career afterwards. a lot of german punk classics, if not most of THE classics.
http://de.youtube.com/watch?v=UwE8dlRnsio
their most well known song I think. translated "destroy what destroys you!"
http://de.youtube.com/watch?v=sa0rpCgVLs4
even if you dont understand the language keep watching. its the TSS drummer talking bout capitalism and anti capitalism...till he, yes tries to destroy the table. that was german Television a few decades ago, hahahah
while grabbng the Mics he says: "I need the mics for some buddies who are in jail" buahahaha
http://de.youtube.com/watch?v=36aoxJYAtn4
mentioned love tune by rio reiser
http://de.youtube.com/watch?v=iM1SvcAfjeQ
the most succesfull track after TSS split up by Rio reiser Solo (highly NDW (New German Wave) influenced)