Learn Hardcore Korean: jeoneun jeonyeogeul meokgo naseo siktageul jeongrihaeyo. - After eating dinner, I tidy up the dining table.

저는 uses the topic marker -는 and means “as for me,” which is natural for describing your usual routine. 제가 uses the subject marker -가 and emphasizes that it is specifically “I” (not someone else) who does it—useful when answering “Who does it?” You can also drop it if the subject is obvious from context: 저녁을 먹고 나서 식탁을 정리해요 is fine.

Does 저녁 mean “dinner” or “evening” here? What’s the difference between 저녁을 and 저녁에?

Here, 저녁을 (object marker) means “dinner” in the sense of “the evening meal.”

저녁을 먹다 = to have dinner.
저녁에 (time particle) = “in the evening” (time of day).
So 저녁을 먹다 is “eat dinner,” while 저녁에 먹다 is “eat in the evening.”

Why do we use 을 after 저녁 and 식탁? Can I omit it?

을/를 marks the direct object. After a final consonant you use 을 (저녁을, 식탁을); after a vowel you use 를. In casual speech, object markers are often dropped when meaning is clear:

With markers: 저녁을 먹고 나서 식탁을 정리해요.
Without: 저녁 먹고 나서 식탁 정리해요.
Both are natural; keeping them is a bit clearer/formal.

What exactly does 먹고 나서 mean? How is it different from just 먹고?

먹고 나서 = “after (finishing) eating, then …” It adds a nuance of completion and clear sequence.
먹고 = “and (then) …” It can also show sequence, and in this sentence 저는 저녁을 먹고 식탁을 정리해요 is perfectly natural. The version with 나서 just emphasizes “after finishing” a bit more.

Can I say 먹은 후에, 먹은 다음에, or 먹은 뒤에 instead? Any nuance differences?

Yes, all work:

먹은 후에: “after eating,” slightly more formal/written.
먹은 다음에: “after/next,” very common and neutral.
먹은 뒤에: “after,” everyday and natural.
먹고서: similar to “after (and then),” often with a nuance of “only after” or emphasizing the order. Your sentence is fine with any of these.

Why not use 먹어서 here? Isn’t -아서/어서 also a connector?

-아서/어서 usually expresses cause/reason or a natural sequence with a cause-like feel.

저녁을 먹어서 식탁을 정리해요 reads as “Because I eat dinner, I tidy the table,” which sounds odd.
To express time sequence (“after doing X, do Y”), use -고 (나서), -은 후에, -은 다음에, etc.

Do the subjects of both parts have to be the same with 먹고 나서?

By default, with -고 (나서) the subject is understood to be the same. If different, make it explicit or use a form that allows subject change smoothly. For example:

Same subject: 저는 저녁을 먹고 나서 식탁을 정리해요.
Different subjects: 가족이 저녁을 다 먹고 나면 저는 식탁을 정리해요. (Here, using -나면 is natural for a subject change.)

What does 정리하다 mean with 식탁? Would 치우다 or 설거지하다 be better?

식탁을 정리하다: to tidy/organize the table (put away dishes, wipe, set things in order).
식탁을 치우다: to clear the table (remove dishes/items).
설거지하다: to do the dishes.
All are common; choose based on what you specifically mean. Many people say 식탁 치우고 설거지해요 for “clear the table and do the dishes.”

What’s the difference between 식탁, 테이블, and 밥상?

식탁: dining table (standard term for the table you eat at).
테이블: loanword “table,” general-purpose; can also be a cafe/desk table.
밥상: traditional low Korean table used on the floor.
In this sentence, 식탁 is the most natural.

What politeness level is 정리해요? How could I say it more formal or more casual? And what about honorifics for “eat”?

정리해요 is the polite informal (-해요) style, common in daily conversation.
More formal: 정리합니다.
Casual with friends: 정리해 or statement style 정리해/정리해.
For honorific “eat,” use 드시다 when the subject is someone you honor:
아버지는 저녁을 드시고 나서 쉬세요.
Since the subject here is “I,” 먹다 is correct.

Any pronunciation tips?

먹고 is often pronounced with a tense sound: [먹꼬].
저녁을 sounds like [저녀글] in connected speech.
식탁을 becomes [식타글].
정리해요 is pronounced [정니해요] due to liaison/assimilation.
A smooth reading: “jeoneun jeonyeogeul meokgo naseo siktageul jeongnihaeyo.”

Is the spacing correct? Should it be 먹고나서 or 먹고 나서?

Standard spacing is 먹고 나서 (separate). Writing 먹고나서 as one word is a common typo online but not standard.

Can I make a more compact everyday version by dropping particles?

Yes. Very natural in speech:

저녁 먹고 나서 식탁 정리해요. You can also omit the topic if clear from context:
저녁 먹고 나서 식탁 정리해요. (still reads as “I …”)
Keep particles in careful writing or when you need extra clarity.