Hi Jo-Anne,
Here is some info that I found on the Emibas CD, this could be the family that you are looking for.
Post 72763
Nilsson, Olof
Bonde (married man)
b. 1/19/1864
Emigrated 2/24/1902
from Enarsvedjan, Offerdal, Jämtlands län (Jämtland)
to Nordamerika
Source: Household Examination Roll, p. 276
Emibas migration file ID: Offerdal Z 1902 002
Post 72764
Olofsdotter, Annika
Hustru (married woman)
b. 3/21/1872
Emigrated 2/24/1902
from Enarsvedjan, Offerdal, Jämtlands län (Jämtland)
to Nordamerika
Source: Household Examination Roll, p. 276
Emibas migration file ID: Offerdal Z 1902 003
Post 72765
Olofsdotter, Maria
Dotter (unmarried woman)
b. 7/4/1897
Emigrated 2/24/1902
from Enarsvedjan, Offerdal, Jämtlands län (Jämtland)
to Nordamerika
Source: Household Examination Roll, p. 276
Emibas migration file ID: Offerdal Z 1902 004
Post 72766
Olofsson, Olof
Son (unmarried man)
b. 3/3/1899
Emigrated 2/24/1902
from Enarsvedjan, Offerdal, Jämtlands län (Jämtland)
to Nordamerika
Source: Household Examination Roll, p. 276
Emibas migration file ID: Offerdal Z 1902 005
Post 72767
Olofsdotter, Ingeborg
Dotter (unmarried woman)
b. 5/29/1901
Emigrated 2/24/1902
from Enarsvedjan, Offerdal, Jämtlands län (Jämtland)
to Nordamerika
Source: Household Examination Roll, p. 276
Emibas migration file ID: Offerdal Z 1902 006
The info on the Emibas CD is of people who registered with the police to emigrate to a foreign country.
Hope this info will be of some use to you in your search for your ancestors.
Have a nice day!
Don