Hello there,
Weel, I have Googled quite a few pages on Orkney self catering,but I can only find the maximum being a farmhouse that sleeps 8.
I think the problem is that most properties on Orkney are either barns,cottages or crofts;which don't usually sleep much over five people.
You might get (say) 5 four bedded cottages,but I get the feeling they wouldn't be together,which could be awkward.
Please bear in mind that Orkney does get tourists,but it is not a place very geared up for tourism.
If the castle isn't TOO expensive it might be an option.
If you want to go to Stronsay then you need to be near Kirkwall as this where the ferries to Stronsay go from.
Do you HAVE to go for Orkney?
I would Google some of the other Scottish Islands and see if they can accomodate a party of 20.
This site:~
http://www.scottscast...h/results-292434.html
does have properties that sleep 20(and over) but not on Orkney,although one (at Ardnamurchan)looks over the Isle of Mull.