When you hit someone with a held object they break, do the Hammers break when you hit with them. I know this sound ridiculous, but my friend ask me, and I immediately said no they don't break, but then I thought about it and so here I am. Do they break?

No. They do not break.

Technically no object breaks. They're just removed from the game when used in an attack. That usually only applies when the character is using Super Strength.

Hammers are Relics and are assigned to a character. The character is never actually "holding" a hammer when they use it in an attack.

The hammers aren't held objects, so no. They go on the charcters' card.