I found this axe in a bandit camp. It says it does extra damage against animals, but unlike most enchanted weapons it has no charge meter on it. Does it have infinite charges, or no charge at all?

I believe it has infinite charges.

It has both infinite and no charge...

To put it simply...

It's basically like an armor enchantment.

Well that's a very unique weapon and so it's got a very unique enchantment.

Infinite charges.
Also, you can disenchant it. However, i don't know if the disenchanted enchantment applied to another weapon has infinite charges too.

It doesn't