An EXP Share is a device that when equipped by a pokemon, earns EXP from fainted pokemon another pokemon in your team caused. You don't have to use that pokemon to level it up if it has an EXP Share!
x4 Lucky Egg
Gives you 4x Lucky Egg
A lucky egg is an item that when equipped by a Pokemon will grant them 50% more EXP given when earning EXP from fainting a Pokemon or by other means.