Hi Gayle,
This is not the right time period but I checked Arkion.
http://www.arkion.se 1890
Homeparish: Tjureda
Residence: L-e-r-i-k-e-m-å-l-a
County: Kronobergs
SVARvolume: 000164 Card nr: 7
Page: 8 Row: 41
Persons in the household
Fam nr: 1
Sven Johan Nilsson f. 1856 in Tjureda, Hem. egare (farm owner)
wife Johanna Katrina Magnusdotter f. 1858 in Ormesberga
s. Karl Gustaf Georg f. 1880 in Tjureda
s. Johan Axel Henrik f. 1883 in Tjureda
Fam nr: 2
widower Nils Peter Svensson f. 1821 in Tjureda, Und. hjon
I suppose that Johan Axel Henrik is your grandfather Axel.
Maybe this is your Axel emigrating in 1903.
First name: JOHAN A
Last name: SVENSON
Age: 19 Gender: M
Parish: ODENSVI County: H (Kalmar)
Port: GÖTEBORG
Date: 1903 03 13
Destination: NEW YORK
Fellows: NEJ
Source: 72:275:2683
They might not have emigrated through a Swedish port. Maybe they used a Danish or German or Norwegian port.
New York (Ellis Island) was NOT the only port used by emigrants to enter the U.S. This site tells more.
http://home.att.net/~arnielang/shipgide.html I assume that C/S is the husförhörslängd, often translated as clerical survey or household examination records.
Have you searched birth, marriage, and death records which can be accessed through the Family History Library through the name of the county (Kronoberg) and then selecting civil registration? Maybe these people could be found through birthdates and those civil registrations extend from 1860-1920. Some are online as SC on the fee-based Genline site.
http://www.genline.com http://www.genline.com/databasen/walk3.php?r=&x=7_100007 I checked the Family History Library online catalog just now for Tjureda parish and much more is available than you say.
http://www.familysearch.org/Eng/Library/fhlcatalog/printing/titledetailsprint.asp?titleno=329345 For example, have you tried ordering the församlingbok, which isn't as good as the husförhörslängd but will list everyone in family groupings until 1925.
Sweden, Kronoberg, Tjureda - Church records
Församlingsbok 1897-1925 AIIa:1-2 - VAULT INTL Film [ 2226088 ]
You can find who moved in and out of the parish from 1895-1911 and where they came from/went to by ordering this film.
Sweden, Kronoberg, Tjureda - Church records
In- och utflyttningslängd 1895-1911 v. BI:2 - VAULT INTL Film [ 2226089 Item 4 ]
Good luck!
Judy