In the medium level there are single colored flashing eggs. Eggs that flash pink (the color of the gryphonette eggs) will feed all of your pets so it's a good idea to save them until some of your pets are hungry. Eggs that flash a teal/blue will heal your pets. It's a good idea to save them in case you need them (they also make it so that your pets are not hungry for a while. Eggs that flash gold will cause all of your pets to lay an egg. Use these as soon as possible so that you can collect the eggs. Eggs that flash green will poison some of all of your pets. (if you have several flashing green eggs on the screen AND a teal flashing egg click on a flashing green to poison your pets and then on a teal to heal them. This will limit the chance of accidentally clicking on it). Eggs that flash black will kill some or all of your pets so refrain from clicking on these eggs at all costs. Eggs that flash purple will kill all monsters on the screen so only click on them when there is a monster.
In the insane level the flashing eggs will flash multiple colors. This means they do multiple things. However, they will never combine good eggs with bad eggs. You will find eggs that will flash gold/purple/pink/teal, pink/purple/gold, green/black and so on but green and black will never be combined with gold, pink, purple or teal.