The Deus Ex Ovum are three eggs which contain the power of Zeus and which can be used to resolve an otherwise hopeless situation with an almost literal deus ex machina. The eggs can only be activated by the patron of Christmas and are one-use only; breaking an egg releases the power within it and sets things right. The Deus Ex Ovum are explicitly stated to contain the "sentient will" of Zeus, and are thus capable of making their own determination about the way things should be. They are most likely successors to Dunuloa's "god spell recorder" egg prototypes.
Two of the Deus Ex Ovum were used before the beginning of Sluggy Freelance. The first is stated to have been used shortly after the fall from power of the Greek gods. The use of the second Deus Ex Ovum is shrouded in mystery, and appears to be related to the first time that Bun-bun was thrown out of time. Basphomy states that it happened when her time was just beginning, but it is not clear whether this refers to the start of her life (assumed to be when she was given life/animation by Dunuloa) or her time as the patron of Halloween. Either way, judging by her reaction, it is much longer ago than Bun-bun's previously assumed lifespan as a slightly abnormal mini-lop rabbit.
The third and final Deus Ex Ovum was used at the conclusion of Holiday Wars. Bun-bun, who had by then become the patron of Christmas, was tricked by 2003 and was forced to use the egg in order to save his life, giving up all of his Holiday powers in the process. Bun-bun menacingly informed the Holidays that they better not mess with him again, as they were now out of eggs, and they responded by once more jettisoning him into Timeless Space.