"The birds are not here yet"and "The birds are still not here" mean essentially the same thing, just with more surprise or impatience in the second sentence. (I see that your German's very good - essentially the same as noch nicht vs. immer noch nicht.) So, unless there is a specific way to express this extra bit of surprise in Turkish, I think the following should added to the allowable answers:
The birds are still not here. The birds still aren't here.
Shinimegami23's sentence doesn't work though because "still" doesn't fit at the end of a sentence like that. These courses from English are super difficult for non-native English speakers.
We do accept "still" as a possibility here to not be too nitpicky but I would still reckon to say that "still" and "yet" have different meanings (as shown by your German above).
One (with still) in a sense implies that the birds should have arrived by now, whereas the one with "yet" implies that you are still awaiting them :)
The one with "still" would be better translated with "daha/hala" in my opinion :)