Goedendag derives from the archaic accusative form "goeden dag", which may mean "(I wish you a) good day".
Goedenavond is also of the same case. But goedemorgen is not in accusative. Sorry, but I do not know why.
PS: The German counterparts of these phrases are all in accusative case.
Very close. Both G's are pronounced differently from English. Depending on where you are from, it can be a voiceless uvular fricative (tongue really far back and makes a hissing noise) or sometimes a voiced velar fricative (tongue like you would say English g but not quite touching). There might also be other pronunciations. I think the first is pretty common.