So, when was Skaði with Oðin long enough for them to have “many sons” together?
The lore records the fact that Oðin was often gone from Asgard for long periods of time. For example: Ynglings Saga chapter 3 states: “Othin had two brothers. One was called Ve, and the other Vili. These, his brothers, governed the realm when he was gone. One time when Othin was gone to a great distance, he stayed away so long that the Æsir thought he would never return. Then his brothers began to divide his inheritance; but his wife Frigg they shared between them. However, a short while afterwards, Othin returned and took possession of his wife again.” Lokasenna also makes reference to this incident, and it’s clear from the lore that Oðin and Frigg had what would be referred to these days as “an open marriage”. Oðin could easily had had a long-running affair with Skaði during one of his long absences. Saxo Grammaticus tells a strange story of how the Æsir made Oðin an outlaw for ten years after his rape of Rind and during this time installed Oller [Ullr] on the highseat in Asgard. I f
