In my opinion, the only answer here that sounds really wrong is D. A is a better, but it would make more sense if it said 'I wasn't listening to music, nor was I eating'. B is correct but sounds a bit more formal and C is correct but quite informal. There are a lot of times where lots of things are being negated, such as:
'I haven't cleaned, cooked or done my homework.'
'I don't like red, blue or green.'
'He doesn't want to go out, talk to anyone or see anyone.'
Hope this helps :)