1. What I saw in the closet left me speechless. = subject
Here, the noun clause is What I saw in the closet. This clause is used as the subject of the sentence. So, you can replace the entire clause with one simple word - he. For example: He left me speechless. This way you can easily determine that the first word (or rather the entire clause in the example above) is the subject.
2. When I was six, I learned how to swim. = direct object
The noun clause here is How to swim. Even though this may look like an adverbial clause, it is not because it has the function of a direct object (which only noun clauses can). You can easily determine that this is a direct object by asking the question - what? For example: What did I learn when I was six? And the answer is: How to swim. This way you know it is an object.
3. I was caught between what my conscience was telling me and what I wanted to do. = object of a preposition
Here, the noun clauses are What my conscience was telling me and what I wanted to do. They are objects, but not regular objects (like in sentence 2 above). Given that they are located after the preposition between, they are called object of a preposition.
4. The scary movie I watched is what kept me awake that night. = predicative nominative
Predicative nominative is a word, phrase, or an entire clause following a linking verb (such as to be, to seem, etc.). In the example above, the linking verb is IS, and the clause following it What kept me awake that night is the predicative nominative.
