Learn Dutch: Wij zijn allemaal moe.

Wij is the emphasized form of we. By using Wij, the speaker puts special focus on the group, perhaps contrasting with someone else (like 'They are energetic, but we are tired'). If there is no special emphasis, you would just say We zijn allemaal moe.

What exactly does allemaal do in this sentence?

Allemaal means 'all' or 'all together' when referring to people or things that are the subject (here, Wij). While English uses 'all' right next to 'we' or after the verb, Dutch uses the adverb allemaal to emphasize that every single person in the group shares the feeling.

Why isn't the word order Wij allemaal zijn moe like in English 'We all are tired'?

In a standard Dutch main clause, the working verb must take the second position. The verb zijn (are) is the second block of information after Wij. Therefore, adverbs like allemaal have to come after the verb.

Since Wij is plural, why doesn't moe get a plural ending?

In Dutch, when an adjective comes after the verb to describe the subject, it never changes its form. It does not get an -e or -s ending, no matter if the subject is singular or plural. It always stays in its basic dictionary form, moe.