Hi Mary & Elisabeth,
First of all, I know that dr is the abbreviation for dräng, don't know what happen there.
Anyway, I have located Karin, not in the birth records for Östmark, but in the census records for that parish. This is the first time that I have come across a missing birth record. I was able to find her with the information you posted Mary. I found her using the subscription site SVAR, In the 1890 census for Östmark, Värmland she was listed as a widow along with a Alfred Söderberg and her son Johan Hultman b 1866.
I will start these GID numbers with Karin Arvidsdotter's family 1836-1840 at GID: 550.27.969, 1841-1845 at GID: 550.15.31600, and then several census record with Karin Jönsdotter b Oct 6 1842 and her family. Starting at 1841-1845 GID: 550.15.30600, which also shows Jöns Ersson's family, then a jump to 1861-1866 at GID: 550.28.26000, 1861-1866 at GID: 550.28.33100, 1866-1870 at GID: 550.30.47800, 1871-1875 at GID: 550.33.59500, 1876-1880 at GID: 550.38.62100, 1881-1885 at GID: 550.40.54500,1886-1890 at 550.42.50100.
You can find Jan Hultman and Karin Jönsdotter's marriage record at GID: 550.20.68100.
Hope this info will help!
Have a nice Day!
Don