Eske: Das große Vornamenlexikon (Duden) says: Fresian pet form, probably of names formed with Old Fresian "es", meaning "Ase (God)".
Svea is as Swedish as can be: The Svear people were one of the Germanic tribes in the early history of Sweden. "Sverige", the Swedish name of the country, means "Svear-rike" (realm of the Svear). The Roman writer Tacitus reports about the Svear in his book "Germania".
A Swedish professor of linguistics from the University of Uppsala told me: Svea probably means something like "of the own people, ourselves" (similar to the original meaning of "deutsch", German).
In modern times Svea became a symbolic character representing Sweden as a whole. In 1670 the artist David Klöcker Ehrenstahl painted "Moder Svea" to the ceiling of the Knights' Hall in Stockholm.
There is a poem by Esaias Tegnér called "Svea" (1811), calling upon Svea to help against the Russians, who had (once more) invaded the country. This time she couldn't help.