Learn Icelandic: Hávaðinn er svo yfirþyrmandi að mig svimar. - The noise is so overwhelming that I feel dizzy.

This sentence uses the svo + adjective + að pattern to show a result. Here, svo pairs with the adjective yfirþyrmandi (overwhelming), followed by the conjunction að (that) to introduce the consequence: the noise is so overwhelming that it causes dizziness.

Why is the pronoun "me" (mig) in the accusative case here instead of the nominative ég?

The verb að svima (to feel dizzy) is an impersonal verb. Instead of taking a normal nominative subject, it forces the person experiencing the dizziness into the accusative case. So, "I feel dizzy" is always mig svimar, which behaves a bit like "it dizzies me".

Does the adjective yfirþyrmandi change its ending depending on what it describes?

No, it does not. Words ending in -andi are present participles, similar to English words ending in "-ing". When used as adjectives in Icelandic, they are indeclinable. This means yfirþyrmandi keeps the exact same form regardless of the gender, number, or case of the noun.

Could I drop the word að in Icelandic, like how we sometimes drop "that" in English?

No, in Icelandic result clauses, the conjunction að is strictly required to connect the two parts of the sentence. You cannot leave it out like you often can in English.