What is the grammatical function of the bolded noun clause in this sentence? While my parents are away, we can do whatever we want.

I suppose the bolded noun clause here is "whatever we want". Its grammatical function is direct object. It signifies the receiver of the action that the subject performs, complementing a transitive verb (a verb that requires an object, e. g. to eat, to drink, to hear, to play, to smell, as opposed to intransitive verbs such as to run, to walk, to sleep, etc.).