Learn Russian: Возьмите этот маленький кусочек сыру.

Here, сыр (cheese) is using the "partitive genitive" (sometimes called the second genitive). Some masculine uncountable mass nouns, like tea (чай), sugar (сахар), and cheese (сыр), can take an -у or -ю ending when you are talking about a quantity or part of them (like a "piece of" or "cup of").

Is it wrong if I just say кусочек сыра instead?

Not at all! In modern Russian, the regular genitive (сыра) is completely correct and actually more common. The partitive -у ending (сыру) sounds a bit more traditional or colloquial. However, you will still hear it often when people offer food, so it is important to recognize it.

Why are этот маленький кусочек in the nominative case if they are the direct object of возьмите (take)?

They are actually in the accusative case! Because кусочек is an inanimate masculine noun, its accusative form looks exactly the same as its nominative form. The pronoun and adjective attached to it (этот, маленький) follow this exact same rule.

Why use the diminutive кусочек instead of just кусок (piece)?

Using diminutives is very common in Russian when offering food or making a polite request. It makes the speaker sound softer, friendlier, and more hospitable than if they used the more neutral or blunt кусок.