Learn Hardcore Indonesian: Orang tua saya sudah cerai.

Literally, orang = person and tua = old, so orang tua means old person.
However, when you say orang tua saya in Indonesian, it almost always means my parents (both of them together), not my old person.

So:

orang tua (or orangtua) = parents (as a set)
orang tua in some contexts can also mean an old person, but usually without a possessive (orang tua itu = that old person).

Context tells you which meaning is intended. In your sentence, sudah cerai clearly shows it refers to two people: your parents.

Why isn’t there any plural ending to show that orang tua means parents?

Indonesian usually does not change the noun to show plural. Plurality is understood from context.

So:

orang = person / people
buku = book / books
orang tua saya = my parent / my parents (context decides)

If you really need to emphasize that it’s plural, you can say:

orang tua saya berdua = my two parents
kedua orang tua saya = both my parents

Can orang tua saya mean just my father instead of my parents?

Normally, orang tua saya means my parents (both).
To refer to one parent, Indonesian usually uses specific words:

ayah / bapak / papa = father
ibu / mama = mother

So you’d say:

Ayah saya sudah cerai dengan ibu saya. = My father has divorced my mother.

In some casual spoken varieties, orang tua can be used more loosely to mean parents or folks in general, but not usually a single parent.

What is the function of sudah here? Could I leave it out?

Sudah literally means already, and it shows that the divorce is a completed event or an existing state now.

Orang tua saya sudah cerai.
= My parents are (already) divorced / My parents have divorced.

If you say only Orang tua saya cerai, it can still be understood, but it sounds less natural and a bit abrupt. Sudah makes the sentence smoother and more idiomatic, especially for a past event that affects the present.

Informal variant:

udah = casual spoken form of sudah
Orang tua saya udah cerai. (very common in speech)

What’s the difference between cerai and bercerai?

Both exist and both are used about divorce, but with slightly different patterns:

cerai (root) is often used in short predicate phrases with sudah/udah:
Mereka sudah cerai. = They are divorced / They have divorced.
bercerai behaves more like a clear intransitive verb:
Mereka bercerai tahun lalu. = They got divorced last year.

In your sentence, Orang tua saya sudah cerai is very natural.
A slightly more formal or textbook-like version is:

Orang tua saya sudah bercerai.

Is cerai here more like a verb (to divorce) or an adjective (divorced)?

It sits somewhere in between from an English point of view.

Grammatically in Indonesian, cerai is a verb root.
In the pattern sudah cerai, it often functions like a resulting state, similar to English are divorced.

So you can think of:

sudah cerai ≈ have divorced / are divorced
It’s not important to label it strictly as “verb” or “adjective” for usage; just remember that sudah cerai is a common way to say are divorced.

How do I say My parents are not divorced or My parents are not yet divorced?

To say not divorced (at all), you can use tidak:

Orang tua saya tidak cerai.
= My parents are not divorced.
(Neutral, just says it’s not true.)

To say not yet divorced (implies it might happen in the future), use belum:

Orang tua saya belum cerai.
= My parents are not yet divorced. / My parents haven’t divorced (yet).

Be careful: belum always carries the idea of “yet / so far”.

Is this sentence formal, informal, or neutral? How would it change in casual speech?

Orang tua saya sudah cerai. is neutral and acceptable in most situations, including fairly polite conversation.

More formal / standard:

Orang tua saya sudah bercerai.

More casual:

Orang tua aku udah cerai.
Ortu gue udah cerai. (ortu is a common abbreviation of orang tua, gue is Jakarta slang for I/me)

So you can adjust saya → aku → gue/gua and sudah → udah to match the level of formality.

Why do I sometimes see orangtua written as one word instead of orang tua?

Both spellings appear:

orang tua (two words) is very common and widely accepted.
orangtua (one word) is also used, especially in writing, with the specific meaning parents (as a unit).

In practice:

orangtua saya or orang tua saya = my parents.
The meaning and pronunciation do not change; it’s mostly a spelling preference. For learners, using orang tua (two words) is perfectly fine.

Where can I add extra information like “my parents divorced when I was little”?

You usually keep the base structure Orang tua saya sudah cerai, then add time or situation phrases after it:

Orang tua saya sudah cerai sejak saya kecil.
= My parents divorced when I was little / since I was small.
Orang tua saya sudah cerai sejak lima tahun yang lalu.
= My parents divorced five years ago.
Orang tua saya sudah cerai waktu saya SMP.
= My parents divorced when I was in junior high school.

The order [subject] + [aspect] + [predicate] + [time/situation] is very typical in Indonesian.