For a change of pace this time, I have a book list for you instead of a poem. These are some books that I would recommend to the modern would-be Asatru alliterative poet, with short commentary on each. Many have references to older languages such as Old Norse or Old English. This is generally unavoidable, as all the great exemplars of the form are in those languages.
1. Hollander, Lee M, trans. Old Norse Poems. London: Abela P, 2010.
2. —. The Poetic Edda. 2nd ed. Austin: U of Texas P, 1962.
Invaluable resources for the alliterative poet, as Hollander translates the old material into Modern English while retaining the original meters as he understood them. His language can be a bit archaic at times, and often sacrifices literal accuracy for the sake of the meter. But the latter is exactly why the alliterative poet should read them. He also includes a brief explanation of the meter in his Edda translation.