I haven't been to Orkney in September but even though some of the migratory birds might have left, or be reduced in numbers, there will still be plenty of residents. It is a superb place and well worth a visit. Although there are a large number of islands it is a relatively compact place and easy to get around. A tour of most of the Mainland could be done easily in a day. Hoy is worth a visit, not only to see the Old Man but there has been a successful breeding of a pair of white tailed eagles this year. Although my visit was in June I got the impression that the place is full of birds - about 50+ species in 10 days, without really trying at all.
It is also a great place for archeological sites. If you are interested in this, I recommend a visit to Rousay.
Dave