Learn Hardcore Turkish: Oda dağınık.

In Turkish, the present-tense copula (the verb olmak, “to be”) is usually omitted in simple descriptive statements. Instead of saying “Oda (is) dağınık,” you simply say “Oda dağınık.” The meaning “The room is messy” is understood without an explicit “is.”

What grammatical case is oda in here?

Here oda is in the unmarked nominative case, functioning as the subject. Turkish often leaves the subject without any special ending when there’s no ambiguity.

Why isn’t there an article like “a” or “the” before oda?

Turkish has no indefinite or definite articles like English. Whether you mean “a room” or “the room” is deduced from context. If you need to be specific you can use:

Demonstratives: bu oda (“this room”), o oda (“that room”)
Possessives: benim odam (“my room”)

Why doesn’t dağınık take an ending like -dir (i.e. dağınıktır)?

The suffix -dir is the formal third-person copula in Turkish, often used in writing or to add emphasis. In everyday speech it’s dropped. So:

Formal/written: Oda dağınıktır.
Colloquial: Oda dağınık.