Even though you didn't bold the noun clauses, it is still obvious which ones they are in these sentences.
1. The noun clause is what I saw in the closet. The function that this noun clause performs is subject. Subject of a sentence is what performs a particular action - in this case, the subject (or the entire noun clause) has left the narrator speechless. If it's confusing, you can replace the clause with a simple pronoun it - It left me speechless, and then it's easier to see it is indeed a subject.
2. The noun clause is how to swim. The function that this noun clause performs is direct object. Direct objects answer the questions whom or what - in this case, you can simply ask - What did I learn when I was six? And the answer would be that entire noun clause - how to swim.
3. The noun clauses here are what my conscience was telling me and what I wanted to do. The function that these noun clauses are performing is object of a preposition. Object of a preposition is really easy to spot - it is a word, phrase, or an entire clause which is located right after a preposition. In this example, the word between is a preposition, and the clauses following it are its objects.
4. The noun clause here is what kept me awake all night. The function that this noun clause performs is predicative nominative. A predicative nominative is a noun, a noun phrase, or a noun clause that is found after a linking verb in a sentence. A linking verb connects two parts of a sentence - here, that verb is is and the clause following it is its nominative.