Learn French: Vous trierez chaque boîte.

No, chaque is invariable. This means it has only one form and never changes, regardless of whether the noun following it is masculine or feminine. Just remember it is always followed by a singular noun, just like the word "each" in English.

If I wanted to say "a few boxes" or "several boxes" instead, how would the sentence change?

You would replace chaque with quelques (a few) or plusieurs (several). But watch out: because those words mean more than one, you must also add an s to make the noun plural. It would become quelques boîtes or plusieurs boîtes.

What tense is trierez?

It is the futur simple (simple future) of the verb trier (to sort). To form the future tense of a regular -er verb, you keep the full infinitive (trier) and add the future ending. For vous, the ending is -ez, giving us vous trierez (you will sort).

Doesn't boîte also mean "nightclub" or "company"?

Yes! In everyday spoken French, une boîte is very commonly used as informal slang for a nightclub or a workplace. However, its literal meaning is simply a "box" or "tin". Since the action here is trier (to sort), "box" is the only meaning that makes sense in this context.