A lot of verses and lines are repeated so would have it been told in song or with accompanying music?
Would there have been accompanying theatrics?
Or would people just have their own tablets and read it like a book?
The tradition of many Mesopotamian societies, especially the Sumerians, was towards a hymn-like form of singing. Now, since the Epic of Gilgamesh is a highly religious text and is at its core highly mythological in formal situations, palaces, temples etc. it would have been recited in a rhythmic monologue, much like modern poetry. Informally it would have most likely been read in a similar manner, almost like a campfire story.
Even the names of Sumerian poetry attest to this form of delivery, like the poem by the priestess Enheduanna In-nin sag gur-ra. This translates to "a hymn to Inana" a Sumerian goddess. You can read it translated here: http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.4.07.3#
Hymns by their very definition imply a rhythmic element to the recital so I think a more poetic and rhythmic delivery is certainly very likely.
I do not think there would be theatrics to go along with it, just a plain delivery by a designated singer, known as the nāru is female and the zammeru if male(Bottéro, Jean (2001). Religion in Ancient Mesopotamia. Chicago: University of Chicago Press.)