Name three uncle-nephew relationships in the poem, and briefly describe how the two relatives treat each other in the poem.
The most significant uncle-nephew relationship is between Wiglaf and Beowulf; Wiglaf is Beowulf's nephew.
Wiglaf is the only one who defends Beowulf in his time of intense need. As Beowulf fends off his final challenge, "No help or backing was to be had then / from his high-born comrades; that hand-picked troop/ broke ranks and ran for their lives / to the safety of the wood. / But within on heart / sorrow welled up; in a man of worth / the claims of kinship cannot be denied. / His name was Wiglaf, a son of Wehohstan's/ a well-regarded Shylfing warrior/ related to Alefrere. (5996-2604; Haney Translation.)
There are other uncle-nephews, I believe Hygelac and Heardred (Geats) and Otherere and Eanmund, but they are not integral (as far as I can tell) to Beowulf's chief narrative. A link to the "Family Tree" is included below.