I am aware of the larger effects the Norse had on the British Isles, but does this go into the artwork as well? It seems to me just through what I've seen over the years that Irish and Norse knot-work is vastly similar. Is it coincidence that both cultures have this art style, or is there a certain reason?
There was a big influence from Scandinavian ornaments to Celtic around 900-1000, it is especially visible in the The Book of Kells manuscript for example. When studying paleografi in Nottingham, a friend learned that it was Scandinavian ornamentation which inspired Celtic to become snirky, and not the opposite which many believe. In the end of the viking age there is a clear influence from styles on the continent in the ornaments, you get Acanthus leaves, rounder shapes etc. Especially in the 50's and 60's it was popular to look for clues of Celtic influence on Norse, but this has been disproven since. But much of that notion still persists. Even though there are proof of earlier trade (before the viking age), the contact was very limited until we started settling there, and even then the contact with Celtic culture was limited. For example, they spoke very different languages. Cross of Cong is another, but later example.
In an viking cemetery in Orkney was found a brooch, which combines styles of both Scandinavian and Celtic art. It's a great piece from the viking age, with 2 inches in diameter. The centre of the piece is now empty but may have housed a piece of amber.
Learn more:
[Celtic art] (http://en.wikipedia.org/wiki/Celtic_art#Iron_Age.3B_Early_Celtic_art)