The following is based on Van Buren and has not been confirmed by canon sources.
At the time of the Great War, ODYSSEUS was an order of magnitude more powerful than contemporary ZAX units. It was designed to coordinate and operate all of the Vaults before the Federal Vault projects were privatized. Poseidon sold the A.I. to the government for use in the maintenance and coordination of Tibbets' Prison, which housed war criminals/deserters who had been exposed to biological weapons or radiation in Denver or in the Yangtze Campaign. Even though it was retrofitted for maintaining the prison and monitoring the prisoners, it still retained an inordinate amount of security clearance. Other than prisoners, no humans were present at Tibbets. ODYSSEUS commanded the all-robot staff, including the seldom-roused ARGOS, who served as the tireless defender of the prison. The government wanted ODYSSEUS to be able to "advise" on the spread of plague vectors in the case of a prison break. This included warming up launch sites like B.O.M.B.-001.
When ODYSSEUS was sold to the prison, its creator became so frustrated that he left Poseidon and started a new project - Diana. ODYSSEUS was the mightiest of all mighty computers. ZAX super computer units were nothing compared to ODYSSEUS, and even though Diana was made by ODYSSEUS' creator, she was developed to be emotionally sophisticated, not powerful.
After the Great War, ODYSSEUS became unstable and developed a split personality. The only "communities" that know of its existence are the machine intelligences governing Robot City to the east, which are attempting to find ODYSSEUS and correct the "divide" that has occurred within its system — and return it to its imprisoned, intended place as their slave.
Presper and his followers released the New Plague virus in the remote areas near Boulder and Denver. It was close enough to the quarantine prison to spur ODYSSEUS into action, but not near enough to huge populations to start a general panic. ODYSSEUS tracked all of the prisoners, so the spread of all the prisoners would alert ODYSSEUS to the various plague vectors. ODYSSEUS was far too secure for Presper to hack, so the only way he could get ODYSSEUS to send the launch codes to BOMB was to lead ODYSSEUS to a logical conclusion: the plague vectors (prisoners) had infected too much of an area for the plague to be conventionally contained. In order to do it, Presper’s men would stage an attack on the prison which would allow everyone to escape. This event would start a countdown of sorts for missile launch on B.O.M.B.-001. ODYSSEUS would assess the viral spread, try to gather up all the escaped prisoners, and once 90% of the prisoners had been retrieved, launch nuclear missiles to “clean & prevent” any further infection.
Repeated attacks from eye-bots revealed to the Prisoner what ODYSSEUS' goal is, which is to continue to send out robots after the prisoners until they all have been brought back to the prison. The eye-bots and ARGOS got everyone pretty quickly - other than the protagonist and six other prisoners. It became obvious pretty quickly that ODYSSEUS is checking people off as they return and kept telling the robots that X more prisoners are unaccounted for, but ODYSSEUS seemed to be unconcerned with prisoners that stream back out again after being captured.
The presumption of the Prisoner was that once all of the prisoners returned, ODYSSEUS would settle down and leave everyone alone. After all of the prisoners were returned it did some massive calculations of where everyone had traveled and it showed that the Prisoner (and the other six prisoners) have spread the Limit-115 to a variety of places. At that point, ODYSSEUS made the determination that the plague was spreading too far, so it armed the B.O.M.B. satellites and melted itself down to try killing all of the prisoners.
The malevolent machine AIs of Robot City, to the east, were hunting down ODYSSEUS for this reason.
ODYSSEUS has not appeared nor is it mentioned in any published game. It was to appear only in Van Buren, the canceled Fallout 3 by Black Isle Studios. It is not certain if it will appear in any future Fallout game.
In later design documents, ULYSSES was renamed to ODYSSEUS. This was done to emphasize the difference between Poseidon's Greek names and Derek Greenway's Roman names. It's possible that Greenway's original name for the computer was ULYSSES but it was eventually renamed ODYSSEUS at Poseidon.