Learn Russian: Он такой глухой, что не слышит этот невыносимый шум. - He is so deaf that he does not hear this unbearable noise.

In Russian, такой is used before adjectives (like глухой) and nouns, while так is used before adverbs and verbs. Even though English translates both as "so", you must use такой because глухой is an adjective.

шум is the direct object of the verb. Why does it look like it is in the nominative case?

It is actually in the accusative case. Because шум (noise) is a masculine inanimate noun, its accusative form is exactly the same as its nominative form. The modifiers этот and невыносимый also follow this rule.

The verb is negated (не слышит). Shouldn't the object be in the genitive case instead of the accusative?

Good catch! After a negated verb, the direct object is often put in the genitive case (этого невыносимого шума). However, the accusative case is also perfectly correct and is frequently used in modern conversational Russian when referring to a specific, definite object like "this" noise.

How is the word невыносимый (unbearable) formed?

It comes from the verb выносить, which means "to endure" or "to bear" (as well as "to carry out"). Adding the negative prefix не- and the suffix -мый creates an adjective that literally means "unbearable" or "unendurable".