Historical context places this episode in 1935. Esther (Grandma) is turning 68. Therefore, she was born in 1867.
The photo of herself that Grandma looks at is a production still of Ellen Corby from I Remember Mama (1948).
Social Security was signed into law by Franklin D. Roosevelt in 1935. Roosevelt speeches used on the Waltons thus far have been recordings of actual FDR speeches; this one is fake in both its text and in voice. An FDR impersonator reads a scripted radio speech that does not match the text of any actual FDR speech.