All the eggs you get from Ovi-elixirs, used on yourself or other NPCs, all result in colored-eggs, which have specific transformative properties based on the color, and amplified in intensity if the egg is large. The eggs are considered unfertilized, and to the best of my knowledge, there is zero way to ever hatch them. Some NPCs can be fed specific colors for their transformations though.
This page on the wiki lists ways to get eggs and their uses at the top, so skip that if you don't want spoilers, but then has a detailed list of the different colors transformative properties.
https://wiki.smutosaur.us/CoC/Eggs