Learn Dutch: Straks gaan we samen eten. - Later we are going to eat together.

This is because the sentence starts with straks (later), which is a time word. In Dutch, the main conjugated verb must always be in the second position. Because straks takes up the first position, the verb gaan comes second, and the subject we is pushed to the third position. This swapping of subject and verb is called inversion.

Could I start this sentence with we instead?

Yes! If you start with the subject we, it takes the first position. The verb gaan stays in the second position, and straks moves after the verb. The sentence would then be: We gaan straks samen eten.

Why is eten (to eat) at the very end of the sentence?

When a Dutch sentence has two verbs, the conjugated verb (gaan) takes the second position, and the second verb (eten) gets pushed to the very end of the sentence in its full infinitive form. You can think of it as a frame around the rest of the words: gaan ... eten.

What exactly does straks mean? Is it "later" or "soon"?

It translates to both! Straks specifically refers to the near future, usually later the same day or in a few hours. If you mean "later" in a much broader sense (like next month, or years from now), you would use the Dutch word later instead.