Eggs
Since version 3.20, all ground nesting birds have laid eggs. Waterfowl like swans and mallards lay eggs on islets and skerries, or near the shore among vegetation, while the ground nesting forest birds, capercaillie, black grouse, willow grouse and hazel grouse, nest in forests. The egg size varies depending on the bird they were laid by, Swan eggs being the largest. Depending on the species, eggs are laid in Swidden (April), Seedtime (May) or Fallow (July).
Eggs are tasty, nutritious and slow to spoil, but don't seem as nutritious as meat cuts. They don't seem to be useful for acquiring meat either, as there are currently no reports of using them as bait luring prey in to traps. Eggs are only edible raw in the unmodded game, but it is possible to mod cooking recipes that have eggs as an ingredient.
When it comes to eggs hatching, according to Sami, the developer, "no (visible) little birds come out from hatched eggs but things are handled (clinically) with bird population adjustments". He also commented that the player's actions shouldn't have an impact on bird populations.
Throwing eggs doesn't break them, but using them to drop squirrels from their treetop hideouts hasn't been tested.
One of Privateer's little mods introduces a bird coop, which allows players to get eggs at home.
Easter was an unknown concept in Iron Age Finland, so the player shouldn't expect to find funky colored eggs laid by a bunny during Easter. It's likely, however, that there were some kind of spring celebrations in Iron Age Finland, but painting eggs was probably not a part of this tradition.