Learn Icelandic: Strákarnir fengu sinn hvorn bílinn.

This is how distributive possession works in Icelandic. Because the grammar focuses on the fact that each individual boy receives exactly one car, the noun bílinn is kept in the singular. It translates neatly to the English concept of getting "one car each".

Why are both parts of sinn hvorn in the accusative case?

When written as two separate words, both parts of the compound pronoun sinn hvor must agree in gender, number, and case with the noun they modify. Since bílinn is a masculine singular noun in the accusative case (as the direct object of the verb fengu), we must use the masculine accusative singular forms for both parts: sinn and hvorn.

Why does bílinn have the definite article when the English translation says "one car"?

This is a strict grammatical rule to memorize: when sinn hvor modifies a noun directly, that noun must take the definite suffix. Even though we say "one car each" in English, the Icelandic phrasing literally builds this as "each their the car".

I've seen this written as the single word sitthvor. Could we use that here instead?