The eggs change every year, so yeah, last year's eggs have expired.
To join the final Goal tournament, you need 20 eggs of each type (100 in total). The lesser tournaments along the way don't have an entry fee.
There are many ways to collect eggs. Check the Announcement:
https://www.conquerclub.com/forum/viewtopic.php?f=1&t=222717#p4928782You can join Easter Scenarios (three different ones!), play games on the Easter map, play regular games (much reduced chance, about equal to purple stars I think), join any or all of the many speed tournaments, participate in the Chat-a-Thon, join Bunny Hopper games, join Rabid Bunny Battle Royales, and of course there's the usual random drops.