Yi is not invulnerable, yi is untargetable. Anything that is already targeted to him will still hit him. Things like AA projectiles (except Kalista),
E,
poison,
Q poison,
R when it hits you (you get the idea)
Master Yi teleports across the battlefield with blinding speed, dealing physical damage to multiple units in his path, while simultaneously becoming untargetable. Alpha Strike can critically strike and deals bonus physical damage to minions and monsters. Basic attacks reduce Alpha Strike's cooldown.
Master Yi teleports to strike up to 4 enemies, dealing 25/60/95/130/165 (+100% Attack Damage) physical damage, with an additional 75/100/125/150/175 damage to minions and monsters. During Alpha Strike Master Yi is untargetable. Alpha Strike can critically strike, dealing an additional 60% Attack Damage physical damage. Basic attacks lower the cooldown of Alpha Strike by 1 second.
Source