Interesting developments.
Think of Rena as a nickname... could be Irene?
Look up your grandmothers death certificate and it should list her birthplace.
One Ancestry I found an Irene in
Irene Soden Baltimore Ward 14, Baltimore (Independent City), Maryland
Irene Sodon Elizabeth City Ward 10, Union, New Jersey
Irene Loden Carbondale Ward 2, Lackawanna, Pennsylvania
Now don't pass off the last name misspellings, transcriptions ar enot always correct. I advise getting the birthplace first, then going back to each of these 1920 census records and reviewing each carefully. : )
If you cannot get hers, ask for your grandfathers. It should still list her. He is listed on Ancestry as well so you can grab his SS and ask the county clerk for the info.