Stan moje sestre je dalje od mog posla.

Because Serbian usually expresses possession with the genitive case.

So stan moje sestre literally means the apartment of my sister, which in natural English becomes my sister’s apartment.

• sestra = sister, nominative
• sestre = sister, genitive singular

After a noun like stan, the person who owns it is often put in the genitive:

• auto mog brata = my brother’s car
• kuća moje bake = my grandmother’s house

Because moja sestra is nominative, meaning my sister as the subject of a sentence.

Here, however, sestre is in the genitive because it shows possession, so the possessive word must match it:

• moja sestra = my sister
• stan moje sestre = my sister’s apartment

The pronoun moj changes form depending on gender, number, and case. Since sestre is feminine singular genitive, the correct form is moje.

It is in the genitive singular.

Breakdown:

• moje = genitive singular feminine form of moj
• sestre = genitive singular of sestra

Together they mean of my sister.

Dalje means farther or further away.

It is the comparative form used when talking about distance.

Related forms:

• daleko = far
• dalje = farther / further

So:

• Stan je daleko. = The apartment is far.
• Stan je dalje. = The apartment is farther away.

Because here Serbian uses the adverbial/predicative form dalje to talk about location or distance.

With je dalje, the meaning is is farther away.

Dalji is an adjective and is used directly with a noun:

• dalji grad = a farther / more distant city

But in your sentence, the natural structure is:

• Stan moje sestre je dalje...

So dalje is the correct choice.

With comparatives, Serbian often uses od + genitive to mean than or from in comparisons.

So:

• dalje od mog posla = farther than/from my work

Other examples:

• Stariji je od mene. = He is older than me.
• Ova kuća je bliže od one. = This house is closer than that one.

So od is the normal word after a comparative like dalje.

Because after od, Serbian requires the genitive case.

So:

• moj posao = my job / my work, nominative
• od mog posla = from/than my job/work, genitive

Both words change:

• moj → mog
• posao → posla

This is very common after od in comparisons.

Because posao has an irregular-looking genitive singular form: posla.

So:

• nominative: posao
• genitive: posla

This is a normal declension pattern for this noun, even though it may look surprising at first.

You should learn it as a pair:

• posao
• bez posla
• od posla
• do posla

Literally, posao means job or work. But in sentences about distance, Serbian often uses it in a way that can sound like my workplace in English.

So depending on context, od mog posla may be understood as:

• than my job/work is
• from my workplace

English often makes that more explicit than Serbian does.

Yes. Je is the 3rd person singular present form of biti = to be.

Here it links the subject to the description:

• Stan moje sestre = my sister’s apartment
• je dalje od mog posla = is farther than/from my work

So je is the normal and necessary copula here.

The subject is Stan moje sestre.

The main noun is stan, and moje sestre tells you whose apartment it is.

So the sentence structure is basically:

• Stan moje sestre = subject
• je = is
• dalje od mog posla = predicate/comparison

This word order is very natural and neutral:

• Stan moje sestre je dalje od mog posla.

Serbian word order is flexible, so other orders are possible for emphasis, but this version is the most straightforward for a learner.

For example, you might hear emphasis changes in speech, but the standard neutral order is the one you have here.

Yes, often it does.

A sentence like X je dalje od Y usually means X is farther away than Y relative to some understood place or person. That reference point may come from the situation or previous conversation.

For example, the speaker may mean:

• farther from my home
• farther from where we are now
• farther from the city center

Serbian can leave that unstated if the context is clear.

In standard Serbian, stan moje sestre is the normal and correct way to express possession.

Using od for possession here would sound unnatural or nonstandard. Serbian usually prefers the genitive without a preposition for this kind of meaning.

So:

• stan moje sestre = correct
• stan od moje sestre = generally not the standard choice here

Very literally, it is:

• Stan = apartment
• moje sestre = of my sister
• je = is
• dalje = farther
• od mog posla = than/from my work

So the literal structure is:

The apartment of my sister is farther than/from my work.

Natural English usually reshapes that as My sister’s apartment is farther from my work or something similar, depending on the context.