Was his wife's name Marian?
The best match for him is a 15 year-old Edward OSWALD, born Minnesota, living iwth his aunt and uncle Ruth and Rolland ROBINSON in St. Paul in 1930. He was reported as having been born in Minnesota, father born Minnesota, mother born Sweden.
This Ruth's maiden name was HEDMAN. I can't tell from the 1930 census whether the aunt or uncle is the blood relative.
A family tree posted by a Rosequist22 includes this Edward OSWALD. It gives his parents' names as Anna E. HEDMAN and Edward J. OSWALD. This Anna's death was listed as 1927.
Minnesota, Marriages Index, 1849-1950
about Edward J Oswald
Name: Edward J Oswald
Marriage Date: 29 Jun 1912
Marriage Place: St Paul, Ramsey, Minnesota
Spouse's Name: Anna E Hedman
Spouse Gender: Female
Event Type: Marriage
FHL Film Number: 1313418
It would take more research, but a good match for the possible father, Edward J. OSWALD, born about 1887 in Minnesota, is found living in Oregon in the 1920 census...
*** The above Edward OSWALD is NOT the correct person. Per the Minnesota Death Index:
Date of Birth: 14 Mar 1915
Place of Birth: MINNESOTA
Mother Maiden Name: HEDMAN
Date of Death: 01 Jul 1959
County of Death: RAMSEY
While it is disappointing not to have found the "correct" Edward OSWALD, it is good that you can rule out future research / references made to this particular Edward.
*** Do you possible names of siblings of your Edward OSWALD? Do you have his marriage certificate? Death certificate?