This Erik didn't come married (based on the Emibas lookup) and this Erik didn't come to the U.S. in 1900 (based on the Emibas lookup), so it doesn't match your family story. However, this Erik was widowed in 1910 and was born about the right time. This Erik had a son with the right name born about the right time (but maybe a year later). I ran out of time to search for him in 1900 but I did find many of the rest of the possible family in the 1900 U.S. Federal Census.
What is the source of your information that he arrived in the U.S. in 1900? The 1910 census (and Emibas) doesn't support that information, assuming I have the right family. Have you found the arrival manifest? Have you found a census or something else to support that year of arrival?
Try using the resources of the Swenson Swedish Immigration Research Center. They have a website (Google it.) but their extensive collection of records is NOT online. We need to go there to research or pay them to research for us. Many of us have found lots about our family there. If they joined one of their churches (They have lots of microfilmed church records.), then the parish of birth is listed.
If they didn't join, they still might have had baptisms, confirmations, marriages, and funerals there, so you might learn who his first wife was in the funeral records (and the membership records, if they joined), and you might find the baptism record for the baby Neils Alfred who was born in Ashtabula. You might find the marriage record for Erik and his new bride, Miss Carlson.
They have microfilms of these church records for Ashtabula.
STATE COUNTY CITY NAME OF CONGREGATION D F FILM # REEL# NOTES
OH ASHTABULA ASHTABULA FAITH LUTHERAN CHURCH L 1881 E-415 MINS1881-1930 OH ASHTABULA ASHTABULA FAITH LUTHERAN CHURCH L 1881 E-416 MINS1896-1922;MEMB1881-1930;M/A'89-30 OH ASHTABULA ASHTABULA FIRST COVENANT CHURCH C 1890 S-804 MINS1888-1928;M/A1914-1943;MEMB'88-28 OH ASHTABULA ASHTABULA MESSIAH LUTHERAN CHURCH L 1921 E-417 MINS1891-1930;MEMB'21-35;M/A'21-35 OH ASHTABULA ASHTABULA SW EV KAPERNAUM CHURCH L 1881 E-415 SEE FAITH LUTH., E-415 & E-416 OH ASHTABULA DENMARK L 1891 E-417 SEE MESSIAH LUTH, ASHTABULA OH
The Swenson Center also has microfilmed newspapers which are useful for obits, etc. They are in Swedish but it is not at all difficult to pick out names and locations and dates. I have seen reports of births, marriages, and deaths and other Swedish news from all parts of the U.S. and Canada and Sweden in these papers, so if you don't find a local paper, try one nearby.
You can copy the obit and ask for help on the Sweden forum so you will know what it says.(Type Sweden into the "Jump to Forum" space at the top right of this page.)
At any rate, it is very difficult to help with no extra clues, so I suggest that you continue to search for more in censuses, the Swenson Center, obits, death certificates, birth certificates, and so forth. Look at this site for ideas of places you can search.