In addition to normal weapons, Blazes can be hurt by snowballs, taking 3 (1 1/2 hearts) per hit. If they have found a way into the Overworld, they are also damaged by water and even rain: Water does roughly 1 damage every second. Like all Nether mobs, they are not damaged by fire or lava.

This gives a blaze 20 health points (because 1 heart = 2 health points). To kill a blaze, you need to inflict 20 points of damage to the blaze.