The Greco-Roman religion, like many faith-traditions rooted in the cultural identity and history of a specific region and people, did not have religious texts as we think of them in the Abrahamic tradition (to which all Westerners are heirs, in cultural perception of what is or is not religious.)

However, there were religious texts in the sense that there were things written down that were ostensibly "religious."

Plays, poetry, biographies of people from pre-history, "histories," and stories concerning the descent of the Roman people, traditions, and institutions, among others, can all be nominally described as religious in the same way the 1998 film Prince of Egypt can be. The stories have set facts with details that can vary between tellings without being incompatible with the wider religious tradition.

While literate societies such as the Romans would and did write these telling down--even the minute details of priestly duties during the various festivals would have been written down by someone--the substance of the Roman religion originated in a pre-literate oral tradition.

It simply didn't ever produce a single unchanging text. Every semi-religious detail, event, or story was being constantly retold and would have many concurrent, similar, but not incompatible forms being tapped by the common people in a still-thriving oral tradition.

One can contrast this with the tradition deriving from Judaism, where the TaNaKh, while undoubtedly inheriting the remnants of an oral tradition in the books of the Torah, was continually, and mostly, developed after most Semitic societies had developed writing, including the Jews. The Jewish tradition, with a direct connection to their god through their priesthood, covenants, prophets, and kings, was always generating new religious substance to record that might not be remembered accurately if it floated around in an oral tradition until a cultural consensus occured--so it was written down sooner rather thab later.

Combine this with active efforts to preserve religious identity in a diasporah, and to directly create a Jewish faith out of a proto-Semitic one under the Kings of Israel, and you end up with a single, largely-agreed-upon text that was compiled together.

And again, to draw a final contrasting line against the Abrahamic tradition, or the religious texts of other not-so-unrelated traditions, such as in Zoroastrianism, the religiously oriented textsof traditions such as the Greco-Roman one are simply recordings of an already existing oral set of stories, myths, beliefs, practices, and events.

Perhaps the lone significant and extant exception is the Aeneid, which redefines the Roman identity around either less popular oral traditions or, in many contemporary circles, entirely fabricated ones. Additionally, there is an entire field of pseudo-geneaology popular among ancient Roman patrician families tracing their bloodlines back to one God or hero or another. But these stories are not, unfortunately, complete records of the oral traditions that certain families might have had.

On a closing note, we should not draw a comparison between the Abrahamic textual tradition and the traditions of the vedas, sriti, upanishads, or other Hindu religions texts. While closer in form and treatment to Abrahamic religious scripture such as the Bible than the Illiad, for example, they are afforded an entirely different position as a body of works than the TaNaKh, Quran, or Christian New Testament are in their respective, exclusive, faith-traditions.