Do you need to have a deity in order to use divine wands? (If you have the proper classes)

Presumably, you're channeling the blessing from the deity of the individual that crafted the wand.

So no.

Which also means that if you follow a deity that doesn't agree with the deity of the person who crafted the wand, you can't use it?

Edit: Rather, also, if you don't give praise to the deity of the person who crafted the wand, too?

No, if you can use the wand feel free to use the wand. Regardless of the original source of the enchantment, you're able to to make use of it.

Some characters may not want to use objects that were empowered by a divine being they're opposed to, though. Likewise, many clerics wouldn't want enemies of their faith using their wands.