Gällinge AIIa:1 (1895-1912) page 107 shows when Johan Anton's siblings moved to the US:
Albin Ludvig born April 18th 1877, emigrated May 15th 1897
August Birger born August 1st 1883, emigrated April 27th 1900
Carl Emil born June 5th 1886, emigrated May 14th 1903
Their mother died August 21st 1904. Her boupp can be found in Fjäre häradsrätt FIIa:112 Ver:a (1904-1904) Bild 4770/sid 70. Unfortunately it only states that all four brothers are living in Amerika. But, at least we know that Johan Anton must be alive then (September of 1904) since he is mentioned.
I have also been thinking about the same family as you have Karen, but I have not found any real proof. All is still circumstantial. That Hilda was born in Brooklyn, New York according to Axel's death record. Her maiden name was Anderson. Are you able to verify this Torbjörn? Do you have more information about Hilda's background?
Most likely Axel's death record:
https://familysearch.org/ark:/61903/1:1:N3WW-CLW Could this be Alberts birth record?
https://familysearch.org/ark:/61903/1:1:NQY3-BF6 Could this be Anton and Hilda's marriage record (they are of the right age)?
https://familysearch.org/ark:/61903/1:1:N7WG-3XV The reason that I think that at least Axel's death record is correct is that I think that I found Carl Emil Johnson's WWII draft registration card:
Name: Emil Karl Johnson
Birth Date: 5 Jun 1886
Birth Place: Sweden
Residence: Chicago, Illinois, USA
Race: White
He is living at 3247 Clifton Ave, Chicago, Cook, Illinois. The person who always know where he is living is Albert Johnson (at the same address). He signs the card with Emil K Johnson.
If you look in the 1940 census Hilda Johnson, her son Albert and her brother in law Emil Johnson lives at that address (note that Hilda is born in New York):
https://familysearch.org/ark:/61903/1:1:K4M5-QYP Torbjörn you also mentioned Colorado. Albin Ludvig Johnson's record in emigranten shows that he was set to go to Denver:
Name: Albin L Johansson
Birth Year: abt 1877
Gender: Man (Male)
Place of Origin: Gällinge Halland Län, Sverige
Destination: Denver Colorado
Record Date: 28 maj 1897 (28 May 1897)
Port of Departure: Göteborg
Database Name: EmiHamn
Archive Call Number: 59:559:5305
Principal Person: Johansson Albin L
He is also in U.S Social Security Applications and Claims Index:
Name: Albin Johnson
SSN: 523050743
Birth Date: 18 Apr 1877
Death Date: 30 Jan 1939
Claim Date: 24 Feb 1939
Type of Claim: Death Claim
Notes: 27 Dec 1978: Name listed as ALBIN JOHNSON
An SSN starting with 523 indicates Colorado. I cannot find him in SSDI though. This is most likely him on findagrave:
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=122110824&ref=acom His WWI draft registration card:
Name: Albin Ludvid Johnson
City: Denver
County: Denver
State: Colorado
Birth Date: 18 Apr 1877
Race: White
Draft Board: 9
He lists Anna Johnson living at the same address as him (3832 Cook, Denver, Colo) as his nearest relative. He works as a car repairer at Burham Station in Denver. I have a theory about this family but I cannot verify by the address. In such case they moved close by before 1920. Let me know if you want the census links I found.
August Birger Johansson was naturalized 1906. From U.S Naturalization Record Indexes:
Name: August B Johnson
Birth Date: 1 Aug 1883
Birth Place: Sweden
Age at Event: 23
Court District: Illinois, Indiana, Wisconsin, Iowa
Year of Arrival: 1900
Date of Action: 26 Sep 1906
His address is 1070 Sheffield Ave, Chicago, Cook. He lists two witnesses:
Anton Johnson at 1070 Sheffield Ave
Andrew V Johnson at 1085 Osgood St. (who is this??)
This is not the address in either the 1900 census, 1910 census or 1920 census for Anton and then Hilda and the children (if they are correct). But they could have moved around as you also write Karen. At least we can conclude that Anton is alive September 26th 1906.
I found a tree on ancestry (doesn't look active though):
http://trees.ancestry.com/tree/39187415/person/19381998190