Sadly, much more information is needed in order to find his Swedish parish. Records were kept in the parish, so to find his birth record (which would name parents), we need the details I asked about earlier.
I suspect he left Sweden with a patronymic last name (ending with son) and not with a surname such as Lindstrand.
Do you have any idea of the maiden names of his wives?
Do you have a complete birthdate? (day/month/year)
Do you know if the children were born in Sweden or was he born in the U.S.? He didn't seem to be traveling with a wife.