From Minnesota Official Marriage System - a record that may (or may not) be relevant:
A groom John Berg married a bride Inga Johnson
16 December 1890 in Hennepin County, Minnesota
Minnesota Marriage Certificate #00490255
The original marriage certificate can be ordered from Hennepin County, but since so little is known about John Berg, it might be difficult to identify whether this is the correct couple.
On Nellie's death certificate, her mother is named as "Inga C." John Berg's first daughter after Nellie's birth is named Clara. Sometimes in Scandinavia a newborn in a second marriage would be named after the first spouse who died. It could be that Inga was Inga Clara - just a possibility.
As I'm sure you know, n Oscar's death certificate his mother's maiden name is given as Simonsen.
Have you located an obituary for John Berg (ca 1857-1933)? I like your description of him as posted on Find a Grave!http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Be...
1905 Minnesota State Census
John Berg 47 b Sweden
Minnie Berg 43 b Norway
Clara A Berg 9 kids born in Minnesota
Oscar D Berg 7
Martin H Berg 4
Vivi (?) A Berg 2
next door to Andrew and Bengta Johnson family b Sweden