sseuregineun hyujirang gati sseuregitonge baro beoryeoya naemsaega an na.

Because -는 marks 쓰레기 as the topic: as for trash...

The sentence is giving a general rule or piece of advice about trash, not just describing one specific action. In Korean, a noun that would logically be the object can still be marked as the topic.

So:

• 쓰레기는 ... 버려야 해 = As for trash, you should throw it away...
• 쓰레기를 ... 버려야 해 = You should throw away the trash...

Both can work, but 쓰레기는 sounds more like a general statement.

Korean often leaves out the subject when it is obvious from context.

Here, the implied subject is something like:

• you
• people
• one

So the sentence naturally means something like you should... or people should... without actually saying you.

That omission is very normal in Korean, especially in advice, instructions, and everyday speech.

휴지랑 같이 means together with tissue / toilet paper / a paper tissue.

A few parts:

• 휴지 = tissue, toilet paper, paper napkin, etc.
  Context decides the best English meaning.
• -랑 = casual and / with
• 같이 = together, along with

So 휴지랑 같이 is literally together with tissue or along with the tissue.

Good question. -랑 by itself can link nouns, but 같이 makes the idea of together / along with more explicit and natural.

Compare:

• 휴지랑 버리다 = throw it away with tissue
• 휴지랑 같이 버리다 = throw it away together with tissue

The version with 같이 sounds a little fuller and clearer. In everyday Korean, this kind of combination is very common.

Here 바로 means right away / immediately / directly.

So it adds the idea that you should not leave the trash sitting around first. You should put it in the trash can immediately.

In other contexts, 바로 can also mean things like:

• right
• exactly
• directly

But in this sentence, right away is the natural meaning.

Here -에 marks the destination/place where something is thrown.

So:

• 쓰레기통에 버리다 = throw it away in/into the trash can

With verbs involving putting or moving something somewhere, -에 is very common.

Examples:

• 상자에 넣다 = put it in a box
• 책상에 놓다 = place it on the desk
• 쓰레기통에 버리다 = throw it in the trash can

버려야 comes from 버리다 + -어야.

In this sentence, it means something like:

• need to throw away
• have to throw away
• must throw away
• only if you throw it away

The exact feel comes from the second clause:

• 버려야 냄새가 안 나
  = You need to throw it away for it not to smell = Only if you throw it away will it not smell

So this is not just a plain command by itself. The following result clause completes the meaning.

Both are possible, but they feel different.

• 버리면 냄새가 안 나 = If you throw it away, it won’t smell
• 버려야 냄새가 안 나 = You need to throw it away for it not to smell / Only if you throw it away will it not smell

So -면 is a more neutral if.

-어야 is stronger. It suggests that this is the necessary condition. In other words, that’s what you have to do to prevent the smell.

Literally, it is closer to a smell doesn’t come out or a smell doesn’t arise.

Korean often uses:

• 냄새가 나다 = to smell, to give off a smell

So:

• 냄새가 나 = it smells / a smell comes out
• 냄새가 안 나 = it doesn’t smell / no smell comes out

This is a very common Korean expression, and it does not match English word-for-word.

Because in Korean, 냄새가 나다 is the standard pattern.

Here, 냄새 is treated as the subject of 나다:

• 냄새가 나다 = smell comes out

That is why Korean uses -가, not -를.

So even though English says it smells, Korean expresses it more like a smell occurs/comes out.

Yes, it sounds fairly conversational.

Casual features include:

• 랑 instead of 와/과
• 안 나 in plain style

A more polite spoken version could be:

• 쓰레기는 휴지와 같이 쓰레기통에 바로 버려야 냄새가 안 나요.

A more formal version could be:

• 쓰레기는 휴지와 함께 쓰레기통에 바로 버려야 냄새가 나지 않습니다.

So the original sentence is natural everyday Korean, especially in speech.

Yes, Korean word order is fairly flexible, as long as the particles stay attached to the right words and the verb comes near the end.

For example, these are similar in meaning:

• 쓰레기는 휴지랑 같이 쓰레기통에 바로 버려야 냄새가 안 나.
• 쓰레기는 바로 쓰레기통에 휴지랑 같이 버려야 냄새가 안 나.

The original order sounds natural and clear, but small changes are possible.

What usually matters most is:

• the particles like -는, -랑, -에, -가
• the final verb position

So Korean relies less on rigid word order than English does.