If you look at version of it online, it's all broken down into verses and stanzas, all numbered. But I wonder if this is how it was originally written down, or if the verses weren't ever marked.
The Elder or Poetic Edda is known entirely from the Codex Regius, a 13th-century collection of Norse poems written on 45 vellum pages. The general form of the text is what we would today call a "wall of text":
(Source: Wikimedia Commons, Public Domain asserted)
(Here's a website that shows pictures of the individual pages a little more closely.)
The poems' textual representation of grouped and numbered lines is done by modern scholars. However this does not imply that the poems have no structure. Their stanzas and lines are naturally deduced from the inherent alliterative verse structure of the words themselves.
Before the poems were written down, of course, they were recited from memory.