Learn Russian: Взрыв был такой сильный, что я закричал от ужаса. - The explosion was so strong that I screamed in terror.

In Russian, так is used to modify verbs and adverbs, but такой is used to modify nouns and adjectives. Because сильный (strong) is an adjective describing the noun взрыв (explosion), you must use такой. Even though it translates to "so strong" in English, Russian grammar essentially says "such strong".

Is the comma before что mandatory, or can I leave it out like we sometimes do in English?

The comma is strictly required. In Russian, subordinate clauses—parts of a sentence that have their own subject and verb, like я закричал here—must always be separated from the main clause by a comma. You also cannot drop the word что the way you can sometimes drop "that" in English.

Why is the perfective verb закричал used here instead of the imperfective кричал?

Закричал focuses on the sudden start of an action or a single completed event (meaning "let out a scream" or "started screaming"). Because the scream was an immediate, sudden reaction to the explosion, the perfective is the right choice. Кричал would mean "was screaming" as an ongoing process.

The English translation says "in terror", but the Russian uses от (from). Why is that?