The Odysseus was a Rebel Alliance vessel, specifically an MC80 Star Cruiser.
Alongside the Zeus and Thor, the Odysseus participated in a convoy operation. This convoy faced an impending assault from Assault Gunboats and TIE Avengers, necessitating the support of X-wings from both Rogue and Blue Squadrons. The starships needed this support to buy sufficient time to jump to hyperspace and escape.
The final result is determined by the player's choice of allegiance.
The Mon Calamari Star Cruisers that appeared in Star Wars: X-Wing vs. TIE Fighter: Balance of Power Campaigns are called MC80a Star Cruisers within the game. However, the 2012 publication The Essential Guide to Warfare later retconned this designation, assigning it to a different cruiser type seen in Star Wars: Episode VI Return of the Jedi.