Two Norse deities can be connected to the álfar, or elves, of Norse myth. One is Freyr, who had Alfheim as a tooth-gift, and was ruler of the álfar. The other is the sun-goddess, whose connection with the álfar runs much deeper than her by-name Álfroðull, or Elfin Beam.
Norse mythology has many puzzles, and one of them is the imbalance in numbers between Aesir and Vanir. The Aesir, who incude Odin and Thor among their number, seem to have many associated gods and goddesses, while the Vanir seem to have only three: Njord, Freyr and Freyja.
Berkana, or Birch, the 18th rune, is often said to be named after the birch goddess. I think however the “goddess” part is modern mythology. Before I go any further I want to say that there’s nothing wrong with that – that’s how mythology gets made. It is interesting to see how ideas get put together and grow into something new.