I present the following as unverified information and would appreciate others who could confirm and supplement any of it.
Erik Westzynthius seems to have a middle name Johan. I am hoping he is the only mathematically inclined Erik Westzynthius in Finland, but there are several Erik Westzynthius' in Finnish genealogy. He was born in Helsinki on March 9, 1901, and had a sister and later a wife, but I have not found any children of his, biologic or academic.
There seem to be contributions by him to Scandinavian actuarial publications as early as 1924, and his name appears (without Johan) in a 1957 Scandinavian mathematical congress roster and also in the 1978 ICM held in Helsinki. He also seems to be acknowledged in a book on surgery for his mathematical assistance; I am searching Google Books using the term "Erik Westzynthius" and am finding only snippets. I have not found any other number theory contributions from him.
The work referenced in the question was communicated to the journal in September 1931 by R. Nevanlinna and E. Lindelof, but it is not clear that this work is what got Erik his fil. dr.; his result was a significant advance in the study of prime gaps however, so my money says it was the Finnish equivalent of his doctoral dissertation. Further, several reviews in different languages of the result appear shortly thereafter, and it isn't long before Erdos and Rankin find improvements.
I am placing this entry as community wiki and invite the MathOverflow community, especially the Scandinavian portion, to improve upon it.
Gerhard "Not Quite The Gentleman Scholar" Paseman, 2012.01.19