In general, reactions interrupt whatever action they are reacting to, but only once that action has been resolved:
Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else’s. The opportunity attack, described later in this chapter, is the most common type of reaction.
When you take a reaction, you can’t take another one until the start of your next turn. If the reaction interrupts another creature’s turn, that creature can continue its turn right after the reaction.
In the case of Wrath of the Storm it happens when you choose to react to this:
When a creature within 5 feet of you that you can see hits you with an
This triggers your reaction, and the enemy's attack has not yet been resolved. Since the trigger happens before the damage (on the hit), it immediately interrupts the enemy's turn, including the damage resolution of the attack. This is in line with how reactions are described above. Thematically, think of it as the cleric exploding with electricity as an immediate response to being struck regardless of the damage the cleric takes in the process.
Note that, even if this kills the enemy, the damage from the hit that triggered wrath of the storm is still calculated.
The spell Shield is a reaction you take when you are hit by an attack. It has additional special properties in the spell description:
An invisible barrier of magical force appears and protects you. Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile.
So in this case, it is a specific exception to the rule that happens as a reaction to an attack that hits you, and it retroactively increases your AC against the triggering attack so that if the attack originally hit you, it might now miss.