In the Old Norse poem Vǫlundarkviša, the background of the story somewhat curiously draws in both swans and elves. The basic myth, as found in the Poetic Edda, tells about the captivity of the smith Wayland (Old Norse Vǫlund) in service of King Nķšušr, and of Wayland's brutal but masterful revenge on the king. But before getting to this main part of the story, the poem tells how Wayland and his two brothers came across three strange maidens, and the three brothers married the three maidens, living together for nine years until the maidens departed off to the north for Mirkwood. (Wayland stayed behind and was captured by Nišušr, leading to the rest of the story, while his brothers were off looking for their lost wives.)
The mythological connections are pretty thick in this relatively archaic poem: the maidens are swan-maidens, and can fly. When the brothers first discover them, their swan-garments lay near them (the Old Norse says Žar vóro hiį žeim įlptarhamir žeira, with the element įlpt-'swan' being a very interesting word linguistically), and the very first words of the poem are about them flying as swans (Meyiar flugo sunnan/ myrkviš ķ gǫgnum'maidens flew from the South/ headed toward Mirkwood'). The three brothers are apparently Elves. Although there is a prose prologue which says they are sons of the Finnish king, the poem itself doesn't mention anything about Finnland, and calls Wayland įlfa lióši'prince of Elves' (10.2a) and vķsi įlfa'ruler of Elves' (32.1b). This poem doesn't say that the swan-maidens are Elves, but does draw a pretty close association between the two types of being.
Also curious is the opening of the story of Kullervo in the Kalevalawhich gives the ancestor of that tragic hero (not an 'Elf' as such - there was no such distinct category in Finnish folklore) as a swan:
A mother reared chicks a great crowd of swans;she set the chicks on the fencebrought the swans to the river.An eagle came, snatched them upa hawk came and scattered them a winged bird strewed them:one it bore to Kareliaone it took to Russian soiland the third it left at home.The one it took to Russiagrew to be a trading manthe one borne to Kareliagrew up to be Kalervo [Kullervo's father]and the one it left at homesprang up to be Untamo [the main villain of the episode]who would blight his father's dayswho would break his mother's heart.-The Kalevala, canto 31, trans. Keith Bosley, p. 432
Tolkien cites this as an example of the 'wealth of mythology' in the world of the Kalevala, and of its 'delightful atmosphere/variety', noting that 'Kullervo, most tragic of peasant boys, is but two generations from a swan' (Kalevala Essay, either draft; TS7 p. 254 and p. 275). As I said, there is no Elvish linkage per se, but this reinforces further the impression that a) swans have a fair mythological significance in the North, and b) the categories between swans and human-like beings are relatively blurry.
I've given these two mythological examples basically as a prelude what I think is a much more interesting linguist web surrounding the words for swans and Elves in Germanic, Indo-European, and Eldarin, which are coming in the next post due to length.