Learn Swedish: Vilka nya strumpor är mina?

Because it describes strumpor (socks), which is plural. When an adjective describes a plural noun, you add an -a to the end of it, making ny into nya.

Why do we use vilka here instead of vilken or vilket?

Vilka is the plural form of the question word for 'which'. Since you are asking about multiple socks, you must use the plural form to match.

What is the singular form of strumpor?

The singular form is en strumpa (a sock). Many en-words that end in -a make their plural by dropping that -a and adding -or.

Why does the sentence end with mina rather than min?

Mina means 'mine' when talking about plural things. Because the socks are plural, the possessive word has to be in the plural form too! If it were just one sock, you would say min.