Learn Russian: Я надеваю носки.

This is a classic rule in Russian! Use надевать when you are putting clothes or accessories ON yourself or someone else (like socks, a hat, or a coat). Use одевать when you are dressing a PERSON or an animal (like dressing a child or a doll). Since you are putting on an item of clothing, надеваю is correct.

What case is носки in this sentence?

It is in the accusative case because it is the direct object (the thing you are putting on). For inanimate nouns in the plural, like носки (socks), the accusative case looks exactly the same as the nominative plural.

Is надеваю perfective or imperfective?

It is imperfective. In the present tense, it means you are in the process of putting on socks right now, or you put them on regularly. If you wanted to say you will put on socks (a completed action in the future), you would use the perfective form: я надену.

What is the singular form of носки?

The singular form is носок (one sock). Notice that when making it plural, the о drops out and the stress shifts to the end of the word: носки.