[The Squatter of Amon Rûdh]

I don't dispute that they are the same word, but it is very dangerous to imply that the Old English form has developed from Old Norse, particularly since Old English was a written language, and middangeard a recorded term even before the first recorded meeting between the two cultures. Since Old English and Old Norse are both descended from the postulated Primitive Germanic, it makes much more sense to assume that the same word developed in two different directions rather than jumping from one language to the other. Notwithstanding that objection, Old Norse literature is at its oldest nearly three-hundred years younger than that of Old English, which makes any such development nonsensical in any case.

In terms of cultural contact, we should not consider the coastal raids of the eighth century as major factors in the development of the English language, particularly minor skirmishes like Portland. Real cultural exchange does not take place between raiders and raided, but between two cultures living alongside one another, as in England after the Scandinavian settlement began in the latter half of the ninth century. It would be a poor historian indeed who projected all the results of centuries of Scandinavian conquest and settlement back to the first recorded Viking landfall in England.

That 'Middle-earth' is a term that existed throughout the Germanic world is reason enough for Tolkien to have used it, in fact I think that was the main reason for his use of it. However, although he mentions the Old Norse form of the word in his letters, he primarily describes it in terms of Old and Middle English, which suggests to me that this was his source for the term.

In terms of influence, the EME midden-erd shows signs of Scandinavian phonology, but the Old English certainly does not. There can be no doubt that they are descended from the same ancestor, but neither is the descendent of the other.