Event Cards are special Arcana Cards whose effects are instantaneous and are played immediately and then removed permanently from play (except Elemental Special Cards) and returned to the box.
If a Great Old One must re-draw a hand and it contains multiple Event Cards, the Great Old One may choose the order in which to play them.
Since these are drawn during the Draw Arcana Phase, these do not count as part of the hand, and so after the effect is determined, the Great Old One continues to draw until they have a full hand.