Learn Russian: Зачем ты постоянно одалживаешь их степлер? - Why do you constantly borrow their stapler?

Because it is a third-person possessive pronoun meaning 'their'. Unlike words for 'my' or 'your', the Russian words for 'his' (его), 'her' (её), and 'their' (их) are indeclinable. They keep their fixed form regardless of the case, gender, or number of the noun they describe.

Why use зачем here instead of почему?

While both translate to 'why' in English, почему asks for a cause or reason, whereas зачем asks for a purpose or goal ('what for?'). The speaker is asking what the person's goal or purpose is in borrowing the stapler.

Can одалживать mean both 'borrow' and 'lend'?

Yes, it is used for both! You have to rely on context. Here, since the person is taking 'their stapler' (их степлер), it clearly means 'borrow'. If the sentence included a recipient in the dative case, it would mean 'lend'.

What case is степлер in?

It is in the accusative case because it is the direct object of the verb. Since степлер is a masculine inanimate noun, its accusative form looks exactly identical to its dictionary (nominative) form.