[4] In June 2017, Jesse Jagz unveiled the album's cover art on his Instagram page; it features a picture of his mother, Lydia Abaga, as a child.

[6] Jesse Jagz performed tracks from the album to select listeners at an Industry Nite event, which was held on June 28, 2017, at Spice Route in Victoria Island, Lagos.

A writer for YNaija described "Alright" as an oversight from the album and a "cheap attempt at nostalgia, filtered through heavy bass and auto-tune".

[4] In a lukewarm review of "Wide and Blue", Debola Abimbolu of Native magazine said the "disjointed narrative between the verses and the hook makes the lyrics unconvincing and the rhymes lacking of the cumulative effect".

In a review for The Native magazine, Debola Abimbolu said Odysseus isn’t a "genre blending masterpiece worthy of Yeezus status nor hip-hop enough to be Illmatic, yet, its aspiration to somehow draw parallels with such projects is admirable enough to be applauded.

"[4] Oris Aigbokhaevbolo of Music in Africa opined that the first half of Odysseus is flawless, but ended the review saying Jesse Jagz did not make a perfect album this time.

"[1] Filter Free Nigeria's Dennis Peter praised the album's production but ended up saying the "average nature of the project left him with a familiar feeling".