Mér líður illa, því ég er með höfuðverk.

Because líða in this meaning uses the dative for the person who experiences the feeling.

So Icelandic says:

• mér líður = I feel / literally something like to me, it feels
• þér líður = you feel
• honum líður = he feels

This is a very common kind of Icelandic structure: the person is not in the nominative (ég), but in the dative (mér).

Líður is the present-tense form of the verb líða.

In this sentence, líða means to feel, especially in the sense of to be feeling physically or emotionally.

So:

• Mér líður vel = I feel well
• Mér líður illa = I feel bad / unwell
• Hvernig líður þér? = How are you feeling?

This is a very useful everyday verb in Icelandic.

Because illa is an adverb, and it modifies the verb líður.

Compare:

• illur / ill / illt = adjective forms meaning bad, ill
• illa = adverb meaning badly, poorly

Since the sentence is describing how someone feels, Icelandic uses the adverb:

• Mér líður illa = I feel bad / unwell

This is similar to the difference between English bad and badly, although English often says I feel bad rather than I feel badly.

It can mean either, depending on context.

It may mean:

• I feel unwell / sick
• I feel awful
• I feel bad emotionally

In your sentence, the second part makes the meaning clearly physical:

• því ég er með höfuðverk = because I have a headache

So here Mér líður illa is best understood as I don’t feel well or I feel unwell.

Here því means because.

So:

• Mér líður illa, því ég er með höfuðverk. = I feel bad, because I have a headache.

A learner should know that því can have other uses in Icelandic too, but in this sentence it is a conjunction meaning because.

A very common alternative is:

• af því að = because

So you may also hear:

• Mér líður illa af því að ég er með höfuðverk.

Because after a subordinating conjunction like því (because), Icelandic usually does not use main-clause verb-second word order.

So in the subordinate clause, the normal order is:

• ég er með höfuðverk = I have a headache

After því, it stays:

• því ég er með höfuðverk

Not:

• því er ég með höfuðverk

This is an important pattern in Icelandic:

• main clauses often show verb-second order
• subordinate clauses usually do not

Literally, it means I am with a headache.

In natural English, of course, that becomes:

• I have a headache

Icelandic often uses vera með (to be with) for temporary conditions, symptoms, or illnesses, for example:

• vera með kvef = to have a cold
• vera með hita = to have a fever
• vera með höfuðverk = to have a headache

So even though it looks strange from an English point of view, it is a very natural Icelandic expression.

Because vera með is very commonly used for temporary states, symptoms, and ailments.

So Icelandic often prefers:

• ég er með höfuðverk = I have a headache

rather than using hafa in the most direct English-like way.

This is one of those places where Icelandic expresses possession in a slightly different, more idiomatic way. For a learner, the safest choice is to remember vera með as a normal pattern for things like headaches, colds, fever, and similar conditions.

It is in the dative, because the preposition með takes the dative.

The dictionary form is:

• höfuðverkur = headache

After með, it becomes:

• með höfuðverk

For this noun, the dative singular happens to look the same as another form, so learners may not immediately see the change. But grammatically, it is dative because of með.

Because Icelandic often does not use an article in cases where English might.

So Icelandic says:

• ég er með höfuðverk

not something that literally corresponds to a headache with a separate word for a.

Also, Icelandic has no indefinite article corresponding exactly to English a/an. That is why bare nouns often appear where English needs a or an.

Yes, absolutely.

• Mér líður illa = I feel bad / unwell
• Mér líður ekki vel = I don’t feel well

Both are natural, but there is often a small difference in tone:

• illa can sound a bit stronger or more direct
• ekki vel can sound a bit softer or less dramatic

In many everyday situations, either one would work.

Because Icelandic punctuation commonly uses a comma before subordinate clauses introduced by words like því.

So:

• Mér líður illa, því ég er með höfuðverk.

This comma is normal in Icelandic writing. English punctuation may be a bit more flexible in similar sentences, but in Icelandic the comma is very common here.