"Avenging and Bright" is by Thomas Moore, 1811. The others are about old historical events, but there's no evidence that the songs are nearly that old. There is an old Irish song of Deirdre/Dierdre's Lamentation, (translated from Gaelic in Kinsalla's 'The Tain') but that isn't one in English for which for which we have the tune. [For sources of tune and text see the Irish tune index on my website.]