Anglo-Saxon poetry was an oral tradition, so one of the best ways to experience it is to read it aloud. Gather a few like-minded friends who have in interest in the old stories, and set up a read-along.
The Anglo-Saxon Riddle Poems are short and fun and a good place to start. Ask folks to bring along two or three they think are particularly interesting or entertaining to share with the group, or provide riddles for people to read aloud while the others try and guess the answer.
Longer poems can spark interesting discussions about the culture: Germanic hero imagery in “The Dream of the Rood,” a story of Christ’s crucifixion, effects of abandonment in “The Wife’s Lament” or consequences of outlawry in “The Wanderer.” Christian images imposed on pre-Christian stories or Germanic ideals presented as Christian virtues can shed some light on the late Pagan/Early Christian worldview of English culture.
For a longer piece, maybe one that continues over more than one meeting, “Beowulf” is the obvious choice. Take turns reading, switching after 20 lines or so.
To select a poem to read, look at various translations and decide which you prefer. Have different people read different translations of the same poem to get a feel for the different styles. Keep in mind that even the Old English version of the poem is only the version that happened to be written down. The story itself would have differed with each performer and performance. For a piece like “Beowulf”, try switching translations every few stanzas. If you know someone who can read Old English, have them do that! If not, find an online recording of the piece you are reading and listen to it in the original language. Even if no one speaks or understands the language, you can still get a feel for the sounds and the rhythm.
Sharing this literature with friends should be fun! Create a safe space where folks can share their love of poetry. Come with an open mind and patience. Not everyone reads aloud with the same skill or comfort. There are no microphones spotlights. Instead of following along line by line, close your eyes and listen. Share mead, beer or beverage of your choice and some snacks. Relax, listen, and let the poetry cast its spell.