...introduce the
Aesir religion into the region (Odin, et al)
Sounds a bit like ASHER, as in the Tribe of, and ASER as quoted by Thor, doesn't it? That would probably put the date somewhat after 620 BC.
"Aesir" is said to be congnate with "Asian" in one of the references. The Aesir religion is said to be influenced by Persian religion. There is another set of gods, e.g. the godess Freya, who are local Scandinavian gods that predate the Aesir.