I had to check if this was in the dictionary. According to Den Danske Ordbog "SPROGBRUG især Jylland". If you say this in København you will sound like a bonderøv ;-)
Calling people bonderøv for sounding like they're from Jutland clearly makes you one. One of the worst things in Copenhagen is meeting someone born and raised Vesterbro who's never been to Jutland and think that makes them cosmopolitan. (And any likely to be a bonderøv than a conservative 7th generation Northern Jutland farmer).
Pia Olson Dhyr, who is a member of the Danish Parliament, said it on Danish television in June 2015. So it can't be all that strange.
Yes, one probably would. I still remember when I was nine years or so and my Danish teacher, Heidi, told me that "træls" was not used on Zealand!
I was an exchange student in Jylland and heard it all the time. Was also surprised when I learned it was "nonstandard"!
Træls is a kind of dialect word used more in the rural part of the country (Jylland/Jutland peninsula) and not so much on the island of Sælland/Zealand where the capital (København/Copenhagen) is. It's debatable if it is standard Danish. You risk sounding like a redneck or worse if you say this in the wrong place ;)
Then what would be an acceptable replacement. Annoying is an extremely common description...i wonder if it's more like if someone says 'y'all' on american tv.