What is your specific question? "Any and all information" is too vague and your replies will probably provide information you already have.
The 1930 U.S. Federal Census shows this Signe whose mother was Ellen Eilerson. Signe was born in Michigan. Ellen was born in Denmark. According to this census, Signe's father was born in Sweden, but he had died by this time. It looks as if Signe might have been married previously since there is a daughter Ellen M. Rasmussen in the household.
More can be seen on the actual census record.
Household Members:
Name Age
Ole Wium 28
Signe Wium 32
Ellen M Rasmussen 12
Ellen Eilerson 65
Source Citation: Year: 1930; Census Place: Detroit, Wayne, Michigan; Roll: 1053; Page: 9B; Enumeration District: 532; Image: 1050.0.
Name: Ole Wium
Birth Year: abt 1902
Birthplace: Denmark
Home in 1930: Detroit, Wayne, Michigan
Relation to Head of House: Head
Spouse's Name: Signe Wium
ame: Signe Wium
[Signe Eilerson]
Birth Year: abt 1898
Home in 1930: Detroit, Wayne, Michigan
Relation to Head of House: Wife
Spouse's Name: Ole Wium
Mother's name: Ellen Eilerson
Name: Ellen M Rasmussen
Birth Year: abt 1918
Birthplace: Michigan
Home in 1930: Detroit, Wayne, Michigan
Relation to Head of House: Stepdaughter
Mother's name: Signe Wium
Name: Ellen Eilerson
Birth Year: abt 1865
Birthplace: Denmark
Home in 1930: Detroit, Wayne, Michigan
Relation to Head of House: Mother-in-Law
==========================================
The 1920 U.S. Federal Census shows that Jens was still alive and apparently this census says he was born in Denmark. (Remember that the father of Signe was Swedish, according to the 1930 census.
Household Members:
Name Age
Jens Eilerson 59
Ellen M Eilerson 56
Source Citation: Year: 1920;Census Place: Grayling, Crawford, Michigan; Roll: T625_760; Page: 27B; Enumeration District: 149; Image: 1099.
Name: Jens Eilerson
[Jens Eilenon]
Age: 59
Birth Year: abt 1861
Birthplace: Denmark
Home in 1920: Grayling, Crawford, Michigan
Race: White
Gender: Male
Immigration Year: 1885
Relation to Head of House: Self (Head)
[Head]
Marital Status: Married
Spouse's Name: Ellen M Eilerson
Father's Birthplace: Denmark
Mother's Birthplace: Denmark
Home Owned: Own
Able to Read: Yes
Able to Write: Yes
Name: Ellen M Eilerson
[Ellen M Eilenon]
Age: 56
Birth Year: abt 1864
Birthplace: Denmark
Home in 1920: Grayling, Crawford, Michigan
Race: White
Gender: Female
Immigration Year: 1887
Relation to Head of House: Wife
Marital Status: Married
Spouse's Name: Jens Eilerson
Father's Birthplace: Denmark
Mother's Birthplace: Denmark
Able to Read: Yes
Able to Write: Yes
===========================================
1920 U.S. Federal Census:
Household Members:
Name Age
Eric E Rasmussen 28
[29]
Signe H Rasmussen 25
Ellen M Rasmussen 2
[2 0/12]
Source Citation: Year: 1920;Census Place: Detroit Ward 8, Wayne, Michigan; Roll: T625_809; Page: 1B; Enumeration District: 259; Image: 31.
Name: Eric E Rasmussen
[Evie E Rasmussen]
Age: 28
[29]
Birth Year: abt 1892
[abt 1891]
Birthplace: Denmark
Home in 1920: Detroit Ward 8, Wayne, Michigan
Race: White
Gender: Male
Immigration Year: 1911
Relation to Head of House: Self (Head)
[Head]
Marital Status: Married
Spouse's Name: Signe H Rasmussen
Father's Birthplace: Denmark
Mother's Birthplace: Denmark
Home Owned: Rent
Able to Read: Yes
Able to Write: Yes
Name: Signe H Rasmussen
Age: 25
Birth Year: abt 1895
Birthplace: Michigan
Home in 1920: Detroit Ward 8, Wayne, Michigan
Race: White
Gender: Female
Relation to Head of House: Wife
Marital Status: Married
Spouse's Name: Eric E Rasmussen
Father's Birthplace: Denmark
Mother's Birthplace: Denmark
Able to Read: Yes
Able to Write: Yes
Name: Ellen M Rasmussen
Age: 2
[2 0/12]
Birth Year: abt 1918
Birthplace: Michigan
Home in 1920: Detroit Ward 8, Wayne, Michigan
Race: White
Gender: Female
Relation to Head of House: Daughter
Marital Status: Single
Father's Name: Eric E Rasmussen
Father's Birthplace: Denmark
Mother's name: Signe H Rasmussen
Mother's Birthplace: Michigan
Able to Read: No
Able to Write: No
=======================================
1910 U.S. Federal Census:
Household Members:
Name Age
Jens Eglerson 48
Ellen Eglerson 46
Sena Eglerson 16
Source Citation: Year: 1910; Census Place: Grayling, Crawford, Michigan; Roll: T624_636; Page: 19A; Enumeration District: 0087; Image: 565; FHL Number: 1374649.
Name: Jens Eglerson
[Jens Ejlerson]
[Yens Ejenson]
Age in 1910: 48
Birth Year: 1862
Birthplace: Denmark
Home in 1910: Grayling, Crawford, Michigan
Race: White
Gender: Male
Immigration Year: 1886
Relation to Head of House: Head
[Self (Head)]
Marital Status: Married
Spouse's Name: Ellen Eglerson
Father's Birthplace: Denmark
Mother's Birthplace: Denmark
Name: Ellen Eglerson
[Ellen Ejenson]
[Ellen Ejlerson]
Age in 1910: 46
Birth Year: 1864
Birthplace: Denmark
Home in 1910: Grayling, Crawford, Michigan
Race: White
Gender: Female
Immigration Year: 1888
Relation to Head of House: Wife
Marital Status: Married
Spouse's Name: Jens Eglerson
Father's Birthplace: Denmark
Mother's Birthplace: Denmark
Name: Sena Eglerson
[Lena Ejenson]
[Sena Ejlerson]
Age in 1910: 16
Birth Year: 1894
Birthplace: Michigan
Home in 1910: Grayling, Crawford, Michigan
Race: White
Gender: Female
Relation to Head of House: Daughter
Marital Status: Single
Father's Name: Jens Eglerson
Father's Birthplace: Denmark
Mother's name: Ellen Eglerson
Mother's Birthplace: Denmark
=========================================
I haven't been able to quickly find this family in the 1900 census. I need to stop now. It is long past lunchtime.
Judy