Eu prefiro água com limão quando estou com dor na garganta.

Yes, eu can be omitted.

Portuguese often leaves out subject pronouns when the verb already makes the subject clear. Since prefiro clearly means I prefer, the sentence could simply be:

Prefiro água com limão quando estou com dor na garganta.

Including eu adds a little emphasis or clarity, but it is not required.

Prefiro means I prefer. It comes from the verb preferir.

This is the 1st person singular form in the present tense:

• eu prefiro = I prefer
• você prefere = you prefer
• ele/ela prefere = he/she prefers
• nós preferimos = we prefer
• vocês preferem = you all prefer
• eles/elas preferem = they prefer

A useful point: preferir is often used directly with a noun, as in:

• prefiro água
• prefiro café
• prefiro chá

In Portuguese, both are possible depending on the context.

Here, prefiro água com limão sounds natural because it means I prefer water with lemon in a general sense. The speaker is talking about a type of drink, not a specific water.

If you said prefiro a água com limão, it would sound more like I prefer the water with lemon, possibly comparing it with some other drink in a specific situation.

So:

• prefiro água com limão = I prefer water with lemon / lemon water in general
• prefiro a água com limão = I prefer the water with lemon, that specific one

Both can exist, but they are not always exactly the same.

• água com limão = water with lemon added to it
• água de limão can sometimes sound more like a lemon-flavored drink or a more fixed expression, depending on context

In everyday speech, água com limão is very natural for plain water with some lemon in it.

So if you mean a glass of water with lemon squeezed into it, água com limão is the safest and most natural choice.

Quando means when.

It introduces the time clause:

• quando estou com dor na garganta = when I have a sore throat / when my throat hurts

So the sentence structure is:

• Eu prefiro água com limão = main idea
• quando estou com dor na garganta = the situation in which that preference applies

This is a very common Portuguese pattern.

Estar com is often used to describe temporary physical states or symptoms:

• estou com fome = I am hungry
• estou com sono = I am sleepy
• estou com febre = I have a fever
• estou com dor de cabeça = I have a headache
• estou com dor na garganta = I have a sore throat / pain in my throat

You may also hear tenho dor na garganta, and it is understandable, but estou com dor na garganta sounds more natural in everyday Brazilian Portuguese for a current condition.

Both can be heard, but they are used a little differently.

• dor na garganta = pain in the throat
• dor de garganta = throat pain / sore throat

In this sentence, com dor na garganta emphasizes the location of the pain: in the throat.

If someone says estou com dor de garganta, that is also very common and often corresponds closely to I have a sore throat.

So both are natural, but:

• dor na garganta is a bit more literally pain in the throat
• dor de garganta is a very common set expression for sore throat

Because na is a contraction.

In Portuguese:

• em + a = na
• em + o = no
• em + as = nas
• em + os = nos

So:

• na garganta = in the throat

This kind of contraction is extremely common in Portuguese and is something learners need to get used to.

Portuguese often uses definite articles with body parts where English prefers possessives.

So Portuguese naturally says:

• dor na garganta = pain in the throat
• machuquei a mão = I hurt my hand
• lavei o rosto = I washed my face

Using minha is possible, but it is usually unnecessary when it is already obvious whose body part is being talked about.

So na garganta sounds more natural than na minha garganta here.

Because the present tense in Portuguese can express a habitual or repeated situation, just like in English.

The sentence means something like:

• Whenever I have a sore throat, I prefer water with lemon.

So even though it is not happening right this second, the present tense works because it describes a regular preference in that kind of situation.

This is very normal in Portuguese.

The original sentence is already natural, but a Brazilian speaker might also say:

• Eu prefiro água com limão quando estou com dor de garganta.
• Quando estou com dor de garganta, prefiro água com limão.

These versions are very common too.

The second one just changes the order for emphasis:

• Quando estou com dor de garganta = when I have a sore throat
• prefiro água com limão = I prefer water with lemon

Água is feminine: a água, uma água gelada, esta água.

Words like água are feminine, but because they begin with a stressed a sound, the singular article is often a rather than something that would sound awkward if repeated. This is similar to a pronunciation-driven pattern.

Examples:

• a água fria
• esta água
• muita água

Notice that adjectives and other words still agree in the feminine:

• água gelada
• água fria

So água is definitely feminine.

A few pronunciation notes for Brazilian Portuguese:

• eu sounds roughly like eh-oo, but as one smooth syllable
• prefiro has stress on fi: pre-FI-ro
• água has stress on the first syllable: Á-gua
• limão has a nasal ending: li-MÃO
• estou sounds roughly like es-TOU
• garganta has stress on gan: gar-GAN-ta

Two especially important points:

• limão ends in a nasal sound, not a fully pronounced English n
• ão is one of the most recognizable nasal sounds in Portuguese

If you want to sound more natural, paying attention to limão and garganta is especially helpful.