Egyrészt nagy a hangerő, másrészt az éjszakai zene sokáig szól.

They form a pair meaning something like on the one hand ... on the other hand or partly ... partly / for one thing ... for another.

• egyrészt = on the one hand / for one thing
• másrészt = on the other hand / for another thing

In Hungarian, they are often used to introduce two different points in an argument or explanation.

So:

• Egyrészt nagy a hangerő, másrészt az éjszakai zene sokáig szól.

means roughly:

• For one thing, the volume is loud; for another, the nighttime music goes on for a long time.

They do not have to express opposite ideas; they can simply list two reasons.

In Hungarian, the verb to be is usually omitted in the present tense, third person singular and plural.

So where English says:

• The volume is loud

Hungarian often says:

• A hangerő nagy
• or Nagy a hangerő

with no separate word for is.

This is completely normal. But in other persons, Hungarian does use the verb:

• Nagy vagyok = I am big
• Nagy vagy = you are big

Only in present-tense third person is it usually left out.

Both are possible, but the word order changes the emphasis.

• A hangerő nagy = The volume is loud/high
  This is more neutral, more like a plain statement.
• Nagy a hangerő = The volume is loud/high
  This puts more focus on nagy (loud/high), as if that is the important point.

Hungarian word order is strongly influenced by focus and information structure, not just fixed subject-verb-object patterns like in English.

So in this sentence, nagy comes first because it is the main thing being highlighted.

Hangerő means volume in the sense of sound level.

It is made up of:

• hang = sound
• erő = strength / force

So the literal idea is something like sound strength.

In everyday Hungarian, hangerő is the normal word for the volume of music, a TV, a speaker, etc.

Hungarian has two forms of the definite article:

• a
• az

Which one you use depends on the sound that follows.

• Use a before a consonant sound:
  • a ház = the house
• Use az before a vowel sound:
  • az alma = the apple

Since éjszakai begins with a vowel sound (é), Hungarian uses az:

• az éjszakai zene

Éjszakai means nighttime, night, or at night, depending on context.

It comes from:

• éjszaka = night

and the adjective-forming ending -i.

So:

• éjszaka = night
• éjszakai = nighttime / nocturnal / happening at night

In this sentence:

• az éjszakai zene

means something like:

• the nighttime music
• the music at night
• music played at night

This adjective is very common in Hungarian:

• iskola = school → iskolai = school-related
• nyár = summer → nyári = summer / summertime
• éjszaka = night → éjszakai = nighttime

In this sentence, it most naturally means music at night or music being played during the night, not a special genre called night music.

The broader context matters, but here the sentence seems to be giving reasons for a complaint:

• the volume is loud
• the music at night goes on for a long time

So éjszakai zene is best understood practically, not poetically.

Sokáig means for a long time.

It is related to:

• soká = for long
• -ig = an ending that often means until / as far as / for (a duration)

In this expression, sokáig is the standard way to say for a long time.

Examples:

• Sokáig vártam. = I waited for a long time.
• Sokáig tart. = It lasts a long time.
• A zene sokáig szól. = The music plays for a long time.

Szól has several meanings in Hungarian, and here it does not mean speak in the usual sense.

Depending on context, szól can mean:

• speak / say / address
• be about
• ring / sound
• play (for music, radio, bells, etc.)

In this sentence:

• a zene sokáig szól

means:

• the music plays for a long time
• the music keeps playing for a long time

So here szól refers to music or sound being heard.

Yes, very often that is the best natural English translation.

• A zene szól. = The music is playing.

In your sentence:

• az éjszakai zene sokáig szól

could be translated as:

• the nighttime music plays for a long time
• the music at night keeps playing for a long time
• the music goes on for a long time at night

All of these are reasonable depending on style.

Because Hungarian adverbs commonly come before the verb.

So:

• sokáig szól = plays for a long time

This is a very normal word order.

Hungarian often places time expressions, manner expressions, and other modifiers before the verb, especially when they are closely tied to it.

Yes, literally it is closer to the volume is big/high.

Hungarian often uses nagy (big) in places where English would use loud or high for volume.

So:

• nagy a hangerő

naturally means:

• the volume is high
• the volume is loud

This is idiomatic Hungarian, even if the literal wording feels unusual from an English perspective.

Yes, very much so.

The structure with egyrészt ... másrészt ... sounds like someone is listing reasons, and the content strongly suggests annoyance:

• the volume is loud
• the music at night lasts a long time

So the sentence feels like part of an explanation such as:

• There are two problems: first, it’s too loud; second, the music at night goes on too long.

Yes, that is grammatically correct, but the emphasis is a little different.

• Egyrészt nagy a hangerő
  Focuses more on nagy — the important point is that the volume is high.
• Egyrészt a hangerő nagy
  Sounds more neutral or more like as for the volume, it is high.

Hungarian often allows more than one word order, but the choice affects what is highlighted.

It is mostly neutral.

• egyrészt ... másrészt ... is a bit more structured and organized than casual everyday speech, because it sounds like someone is laying out an argument.
• The rest of the sentence is ordinary, standard Hungarian.

So it would fit well in speech or writing when someone is explaining their reasons clearly.