Jean, the emigration dates doesn't fit exactly, but this is what I found.
Karlskoga (T) 1880-08-13 Lennström Albert Erik, Bofors, born 1859-03-02 Köping (H or U)
Left Göteborg 1880-08-20 destination Chicago.
Karlskoga (T) 1881-08-24 Lennström Anders Erik, Millworker, Bofors, born 1831-01-14 Gällersta (T)
Karlskoga (T) 1881-08-24 Lennström Gustaf Edvin, Bofors, born 1862-07-06 Kloster (H or W)
Left Göteborg 1881-06-03 destination Chicago
Karlskoga (T) 1881-08-24 Wretström Karolina Wilhelmina, Millworkers wife, Bofors, born 1837-07-08 Köping (U)
Karlskoga (T) 1881-08-24 Lennström Alfred Edvard, Bofors, born 1865-12-30 Vimmerby (H)
Karlskoga (T) 1881-08-24 Lennström Karl Hjalmar, Bofors, born 1870-09-16 Vimmerby (H)
Karlskoga (T) 1881-08-24 Lennström Hilma Albertina, Bofors, born 1872-10-11 Härnösand (Y)
Karlskoga (T) 1881-08-24 Lennström Oskar Helmer, Bofors, born 1875-04-02 Härnösand (Y)
Karlskoga (T) 1881-08-24 Lennström Elin Maria, Bofors, born 1878-01-04 Piteå (BD)
Karlskoga (T) 1881-08-24 Lennström Hilda Karolina, Bofors, born 1880-01-16 Karlskoga (T)
Left Göteborg 1881-09-16, destination New York.
The family did move around Sweden, from South to North. Also, it seems that Anders Erik and Gustaf Edvin left before the move was reported to the parish and then sent for the rest of the family.
The Emigrant listing for Örebro can be downloaded from
http://hem.passagen.se/palmestal/avskrifter/avskrifter_frames.htm The leaving dates from Göteborg from the CD 'Emigranten'. The ships name is not listed, the normal route was from Göteborg to Hull, England and then from Liverpool to US. Wilson Line steamships 1880/1881 from Göteborg was Orlando, Romeo, Marsdin, Rollo, Hero, Argo, Bravo, Cameo, Domino, Kelso, Pacific, Nero and Otto.
Rgds. Bo.