Since I'm not sure what you've already searched or not, the first thing I did was try to find your family on the 1920 and 1930 censuses:
1920 Nebraska, Lancaster County, Lincoln, ED 82, Page 7B.Enumeration Date: 10 Jan 1920.
Dwelling 183/Family 186.3087 Vane ST (rents)
George A Mathews, head, white, 40, married, reads, writes, b LA, parents b VA, traveling salesman for chemical company
Estelle M, wife, white, 31, married, reads, writes, she and parents b KY
Bonita J., daughter, 10, reads, writes, attends school, b Illinois
George R., son, 7, attends school, b Ill
Jacqueline J., daughter, 1 yr 6 months, b Nebraska
1930 CA, Los Angeles County, Long Beach, Page 1B. Dwelling 30/Family 30.(rents for $35).This family owns a radio.
George A. Mathews, head, white, 51, married, age 25 at first marriage, reads, writes, b Illinois, parents b US, salesman
Estelle, wife, white, 40, married, age 17 at first marriage, b Kentucky, parents b Kentucky, saleslady
Bonita, daughter, white, 20, reads, writes, b Illinois
George Jr., son, white, 17, reads, writes, b Illinois
Jacqueline, daughter, white, 11, reads, writes, b Nebraska
It looks like you may have already seen the 1920 census, since it matches the birthplaces that you gave.The 1930 census doesn't agree, though.
I checked the 1880 census index (available for free at www.familysearch.org), and I could find Will and Georgianna in LA.Since the 1930 census said that George was born in Illinois, I decided to try looking there too -- and I think I found them!
1880 Illinois, Dekalb County, ED 31, Page 91C.
Dwelling 124/Family 131.
William H. Mathews, white, 35, head, Jeweller, he and parents b NY
Georgianna, wife, white, 34, keeping house, b Canada, father b England, mother b Scotland
Nellie, daughter, white, 5, at home, b Illinois
George A., son, white, 2, at home, b Illinois
Renozen? Staten, white, male, 24, at school, b NY, parents b Virginia
This is interesting, because it lists different birthplaces yet again for Will and Georgianna.Don't you just love the fact that census birthplaces and ages are so flexible?It's caused me no end of grief in my searches too.
I checked the 1870 census index, and only 1 Georgianna Main was listed (with yet another birthplace).Of course, it is still possible that Georgianna was born in Canada and hadn't moved to the US yet.
1870 Maine, York County, York, Page 16.
Dwelling 135/Family 139.
Asenath Main, 66, white, female, keeping house, $2000 real estate, $500 personal property, b Maine
Georgianna Main, 24, white, at home, b Maine
and living 2 doors down...
Dwelling 133/Family 137
Wallace Main, 37, white, works in brick yard, $600 real estate, b Maine
Charles W., 14, at school, b Maine
Lizzie J., 9, at school, b Maine
George B., 4, at school, b Maine
Hannah Wilson, 34, keeping house, b Maine
This same family was listed in the 1860 and 1850 censuses in Maine:
1860 Maine, York Couny, York, Page 965.
Dwelling 1033/Family 1090.
Asceneth Maine, 56, female, 1400 real estate, $150 personal property, b Maine
Georgia V., 14, b Maine
Dwelling 1034/Family 1091.
Wallace Maine, 27, farm laborer, $50 personal property, b Maine
Catherine, 29, b Maine
Charles W., 5, b Maine
1850 Maine, York County, York
Dwelling 221/Family 221.
Zeneth Maine, 44, $175, b Maine
Albert Mc Intire, 21, laborer, $1500, b Maine, married within the last year
Lydia McIntire, 24, b Maine, married within the last year
John Maine, 19, laborer, b Maine
Wallace Maine, 17, laborer, b Maine
George Maine, 4, female, b Maine
I know this is a lot of information, and I hope some of it is useful for you.