You might be able to make some connections online, but more information would be very helpful, so if you have any, please reply.
Try this census search page for 1865, first name type in Ole, farm name, type in Aukland. That produces four Ole's from Aukland farms. See if any of those look familiar based on family members or birthdates:http://draug.rhd.isv.uit.no/folketellinger_engelsk_britisk.h...
Most homesteading in Minnesota occured after the Civil war.
You might also want to contact the Norwegian emigration center in Stavanger, webpage:http://www.utvandrersenteret.no/index_eng.html
But try finding out more information here in Minnesota - from census records, the local historical society of the town he lived in or county, and his obituary or church records. Then you'll have more to go on. Especially if you've ever heard that he possibly used a different last name and "changed" it to Aukland. Like, "it used to be Anderson, but he changed it to Aukland" or some such. If you've heard that there might have been a name that ended in -son or -sen, that could give a clue as to who his father was. Also, have you checked with all of the US relatives that you can find? There might be a genealogist in the group somewhere, and you would be duplicating their work that might already be done.
I did find an Ola (alternative spelling of Ole) Gudmundsen Aukland emigrating out of Stavanger, but there is no date that I can tell.http://digitalarkivet.uib.no/cgi-win/webcens.exe?slag=n&...
There is a census for Minnesota Norwegians in 1880. I found this family, but the spelling is Okland, with the father Ole O.
Is this the family? If so, it gives some approximate dates, if not, rule them out. (Approx. birthdates of Ole, and the kids were all born in Minnesota, so they were here since at least 1868.) http://digitalarkivet.uib.no/cgi-win/webcens.exe?slag=n&...
There is also a farm name spelled Ã¸kland, and I have seen the letter Ã¸ be changed to just an o, or to an au.
Good luck, I hope I gave you some possibilities, but no I don't think there were any certainties!