Meu olho dói.

Because olho is a masculine singular noun. In Portuguese, the possessive has to agree with the noun:

• meu olho = my eye
• minha mão = my hand

So meu goes with masculine singular nouns, and minha goes with feminine singular nouns.

Dói is the third-person singular form of the verb doer = to hurt / to ache.

The subject here is meu olho = my eye, which is singular, so the verb must also be singular:

• Meu olho dói. = My eye hurts.
• Meus olhos doem. = My eyes hurt.

Even though the person feeling the pain is I, the grammatical subject is my eye.

A little, yes. In Portuguese, the thing that hurts is very often the subject:

• Meu olho dói.
• Minha cabeça dói.
• Meu braço dói.

This is similar to English My eye hurts, but Portuguese uses this pattern very naturally and often.

Also, doer usually means to ache / to be painful, while machucar usually means to injure / to hurt physically.

So:

• Meu olho dói = my eye hurts / aches
• Machuquei o olho = I hurt/injured my eye

Yes. That is very natural in Brazilian Portuguese.

• Meu olho dói = my eye hurts
• Meu olho está doendo = my eye is hurting

The version with está doendo emphasizes that the pain is happening right now. In everyday spoken Brazilian Portuguese, tá doendo is extremely common:

• Meu olho tá doendo.

You cannot normally say just olho dói. That sounds incomplete.

Portuguese usually needs a determiner with a singular countable noun, so you would say something like:

• Meu olho dói
• O olho dói
• Meu olho está doendo

So the problem is not the word order; the problem is that bare olho sounds unfinished here.

Yes. O meu olho dói is also correct.

In Brazilian Portuguese, the definite article before a possessive is often optional:

• meu olho
• o meu olho

Both are possible. The version without the article is shorter. The version with the article can sound a little more specific or emphatic, depending on the speaker and context.

Because Portuguese often uses the definite article with body parts when it is already obvious whose body part is being talked about.

For example:

• Machuquei o olho. = I hurt my eye.
• O olho tá doendo. = My eye is hurting. / The eye hurts.

English usually prefers my, but Portuguese often does not need to repeat ownership if the context already makes it clear.

So meu olho dói is correct, but o olho dói can also be natural in the right context.

Dói is pronounced roughly like doy, rhyming with English boy, but starting with d.

It is one stressed syllable: DOY.

The accent mark in dói helps show the stressed vowel quality. It is not optional in normal spelling.

Because the subject of the sentence is meu olho, not I.

The sentence is built around my eye as the thing that hurts. So Portuguese does not need a separate I here.

Also, Portuguese often leaves out subject pronouns when they are not necessary, but in this sentence the main reason is simply that my eye is the grammatical subject.

Everything becomes plural:

• Meu olho dói. = My eye hurts.
• Meus olhos doem. = My eyes hurt.

The changes are:

• meu → meus
• olho → olhos
• dói → doem

Yes. A very common alternative is:

• Estou com dor no olho.
• In casual speech: Tô com dor no olho.

Literally, this is I am with pain in the eye, but the natural English meaning is My eye hurts or I have pain in my eye.

This is one of the most common everyday ways Brazilians talk about pain.