Ég hlusta oft á þetta lag á leiðinni í vinnu.

In Icelandic, hlusta normally takes the preposition á when you say what someone is listening to.

• hlusta á lag = listen to a song
• hlusta á mig = listen to me

So á is not optional here. It is part of the normal pattern of the verb.

That is the normal word order in a main clause.

Icelandic usually follows a verb-second pattern in main clauses. Since Ég is the first element, the finite verb hlusta comes second, and the adverb oft comes after it:

• Ég hlusta oft ...

If you move oft to the front, the verb still has to stay second:

• Oft hlusta ég á þetta lag ...

But Ég oft hlusta ... is not the normal word order.

Because lag is a neuter singular noun, and the demonstrative þessi changes form to match the noun’s gender, number, and case.

Here the forms are:

• masculine: þennan / þessi / þessum etc.
• feminine: þessa / þessi / þessari etc.
• neuter: þetta

So:

• þetta lag = this song

It is accusative, because hlusta á takes an object after á in the accusative.

So in this sentence:

• á þetta lag

The tricky part is that lag is a neuter noun, and in the singular its nominative and accusative forms are the same. So you do not see a visible change in lag itself here, but grammatically it is accusative.

Literally, it means on the way.

The noun is leið = way, route, path. In this expression, Icelandic uses:

• á leiðinni = on the way

This is a very common idiomatic phrase, especially in expressions like:

• á leiðinni heim = on the way home
• á leiðinni í skólann = on the way to school

Because this phrase uses the dative singular definite form of leið.

Here is what is happening:

• leið = way
• leiðinni = the way / on the way

The ending -inni shows both:

1. the dative singular
2. the suffixed definite article

After á, when the meaning is location or position rather than motion across/onto something, Icelandic often uses the dative. In á leiðinni, the phrase is idiomatic and fixed, so learners usually just learn it as a chunk: á leiðinni = on the way.

Í vinnu is the natural idiomatic way to say to work or at work in many everyday expressions.

In Icelandic, words like work, school, and similar routine destinations are often used without the definite article when speaking generally.

So:

• í vinnu = to work / at work
• í skóla = to school / in school

Using í vinnuna would sound more like referring to a more specific workplace or the workplace as a concrete destination, rather than the general routine idea of going to work.

You know it from the meaning and the preposition rule, not from the form itself.

The preposition í works like this:

• motion into / toward something → accusative
• location in something → dative

In á leiðinni í vinnu, the meaning is directional: on the way to work. So it is understood as accusative.

The reason this is hard to see is that vinna is a noun whose singular forms look the same in more than one case:

• accusative singular: vinnu
• dative singular: vinnu

So the form alone does not tell you; the sentence structure does.

Because Icelandic often leaves out possessives when they are obvious from context.

English often says:

• on my way to work

But Icelandic very naturally says simply:

• á leiðinni í vinnu

It is understood that this means the speaker’s usual work unless the context says otherwise. Adding mína or some other possessive would usually only be done for emphasis or contrast.

No. They are two different uses of the same preposition.

1. hlusta á þetta lag
   Here á belongs with the verb hlusta and means listen to.

2. á leiðinni
   Here á is part of the fixed expression meaning on the way.

So even though the word is the same, the grammar is different in each part of the sentence.

Because Icelandic often uses the simple present where English also uses a simple present, especially for habits.

This sentence describes something habitual:

• I often listen ...

So the plain present hlusta is exactly what you would expect.

Icelandic does have ways to express an ongoing action, such as vera að + infinitive, but that would give a different nuance:

• Ég er að hlusta ... = I am listening right now / in the process of listening

That is not the idea here. Here the meaning is a repeated habit, so Ég hlusta oft ... is the natural choice.