Ilman unta olen väsynyt.

Because ilman (without) requires the partitive case in Finnish.

• uni = sleep (dictionary form, nominative)
• unta = sleep in the partitive (used after ilman)
  So ilman unta literally means without (any) sleep.

Unta is the partitive singular of uni. Common singular forms:

• nominative: uni
• genitive: unen
• partitive: unta
• inessive (in sleep): unessa This sentence uses partitive because of ilman.

It most naturally means without sleep / lacking sleep, and in everyday use it often implies not getting sleep (enough). Context decides whether it’s:

• no sleep at all (e.g., stayed awake all night), or
• insufficient sleep (e.g., too little sleep)

Finnish verb endings show the subject, so the pronoun is often omitted.

• olen already means I am (1st person singular of olla, to be)
  You can say Minä olen väsynyt, but it adds emphasis (like I as opposed to someone else).

Olen is the present tense, 1st person singular form of olla (to be). Present tense:

• minä olen = I am
• sinä olet = you are
• hän on = he/she is
• me olemme = we are
• te olette = you (pl) are
• he ovat = they are

In this sentence it functions as an adjective meaning tired, but it’s historically the past participle of the verb väsyä (to get tired). Finnish commonly uses participles as adjectives:

• olen väsynyt = I am tired (literally I am become-tired)

Adjectives agree with the noun/pronoun they describe when they are in a case. Here, väsynyt is a predicate adjective after olen, and it stays in the nominative singular:

• (Minä) olen väsynyt. If the subject were plural:
• Me olemme väsyneitä = We are tired (predicate often uses plural partitive)

Both are possible, with slightly different emphasis.

• Ilman unta olen väsynyt. = Without sleep, I’m tired (focus on the cause)
• Olen väsynyt ilman unta. = I’m tired without sleep (sounds a bit less natural; you’d more often say the cause first) Finnish word order is flexible and often used to manage emphasis.

Yes, depending on what you mean:

• En ole nukkunut, joten olen väsynyt. = I haven’t slept, so I’m tired.
• Nukkumatta olen väsynyt. = Without sleeping, I’m tired. (more literary/compact)
• Huonosti nukuttuna olen väsynyt. = After sleeping badly, I’m tired. But Ilman unta olen väsynyt is correct and understandable.

Yes. Ilman + partitive is a common pattern:

• ilman rahaa = without money
• ilman ruokaa = without food
• ilman apua = without help
  Same grammar as ilman unta.

Usually no comma is needed:

• Ilman unta olen väsynyt. A comma could appear in some stylistic cases (especially in longer sentences), but in a short sentence like this, it’s typically written without one.