Í lok dagsins vil ég bara sofa.

Because Icelandic normally follows a verb-second pattern in main clauses.

Here, the sentence starts with the time phrase Í lok dagsins. Once that comes first, the finite verb usually has to come next:

• Í lok dagsins vil ég bara sofa.

So the order is:

• first: Í lok dagsins
• second: vil
• then: ég

If you start with the subject instead, then you get:

• Ég vil bara sofa í lok dagsins.

That is also grammatical, but the emphasis is a little different. The original sentence highlights at the end of the day first.

Dagsins is the genitive singular definite form of dagur meaning day.

The pattern is:

• dagur = a day
• dags = of a day
• dagsins = of the day

In í lok dagsins, the noun lok is followed by a genitive phrase, so dagsins means of the day.

So literally, the phrase is something like:

• í lok dagsins = in/at the end of the day

A rough word-for-word breakdown is:

• Í = in / at
• lok = end
• dagsins = of the day

So the phrase literally means at the end of the day.

This is a very useful expression for talking about the final part of a day in a literal time sense.

Because vilja normally takes a bare infinitive in Icelandic.

So you say:

• ég vil sofa = I want to sleep

not:

• ég vil að sofa

This is similar to how English says I want to sleep without to being marked separately after a modal-like structure in Icelandic grammar.

So in this sentence:

• vil = want
• sofa = sleep

and sofa stays in the infinitive without að.

Vil is the 1st person singular present tense of vilja, meaning to want.

So:

• ég vil = I want

This verb is somewhat irregular, so it is worth memorizing as a whole pattern rather than expecting it to behave like a fully regular verb.

In this sentence, vil ég still means I want; the subject just comes after the verb because of the word order rule.

Bara usually means just, only, or sometimes simply, depending on context.

In this sentence, it gives the sense:

• I just want to sleep
• All I want to do is sleep

It adds a feeling of simplicity or exhaustion: nothing complicated, nothing extra — just sleep.

Yes, bara is fairly flexible, but moving it can slightly change the emphasis.

In your sentence:

• Í lok dagsins vil ég bara sofa.

This most naturally means At the end of the day, I just want to sleep.

You could also say:

• Ég vil bara sofa.
• Ég bara vil sofa.
  This is much less natural in ordinary speech.

The most natural position is often before the infinitive or the thing being emphasized:

• vil bara sofa

That keeps the focus on just sleeping.

Not necessarily.

In this sentence, í lok dagsins is most naturally understood literally: the final part of the day.

English at the end of the day can also be an idiom meaning ultimately or when everything is considered. Icelandic does not always use í lok dagsins in exactly that same abstract, idiomatic way.

So here, you should understand it as a real time expression:

• when the day is ending
• by the end of the day
• at the end of the day in the literal sense

Yes, it is natural and clear.

It sounds like something a person might say when they are tired and want rest:

• Í lok dagsins vil ég bara sofa.

It has a slightly expressive feel because the sentence begins with the time phrase. That puts emphasis on when this feeling happens: by the day’s end, the only thing I want is sleep.

A rough English-friendly approximation is:

• ee lohk DAHG-sins vil yeh bara SOH-va

A few helpful notes:

• Í sounds like a long ee
• g in ég is not a hard English g
• sofa is SOH-va, not like English sofa the furniture

If you want a more careful learner breakdown:

• Í
• lok
• dagsins
• vil ég
• bara
• sofa

Listening to native audio is especially helpful here, because Icelandic pronunciation does not always match what an English speaker would expect from the spelling.