Learn Dutch: Sorteer jij vanavond kleren? - Are you sorting clothes tonight?

This is because of the rule for placing objects relative to adverbs. Because kleren (clothes) is indefinite here—meaning just clothes in general, not "the" clothes—it must come after the time adverb vanavond (tonight).

How would the sentence change if I wanted to say "Are you sorting the clothes tonight?"

If you are talking about specific clothes, you make the object definite by adding de (the). Definite objects move in front of time adverbs in the middle of a Dutch sentence. The sentence would become: Sorteer jij de kleren vanavond?

Why is the verb sorteer and not sorteert? Doesn't jij normally get a -t?

Yes, normally jij gets a -t added to the verb stem, as in jij sorteert. However, when you ask a yes/no question and jij or je comes directly after the verb, you drop that -t. That is why it becomes Sorteer jij.

Is kleren related to the word kleding? What is the difference?

Yes, they both refer to clothes. Kleren is a plural noun (just like "clothes" in English), whereas kleding is an uncountable singular noun (like "clothing" or "apparel"). You will hear kleren used much more often in everyday spoken Dutch.