Ég tek heyrnartólin með mér í strætó á morgnana.

Taka is the infinitive, meaning to take.
Tek is the 1st person singular present tense form, used with ég.

So:

• að taka = to take
• ég tek = I take

This is just normal Icelandic verb conjugation.

The ending -in is the definite article attached to the noun.

So:

• heyrnartól = headphones
• heyrnartólin = the headphones

In Icelandic, the definite article is often added to the end of the word instead of being a separate word like English the.

It is usually treated as a plural noun, much like English headphones.

That means heyrnartólin is best understood as the headphones, not the headphone.

In this sentence it is the direct object of tek, so it is in the accusative, but for this neuter plural noun the form looks the same as the nominative.

Because the preposition með takes the dative in this meaning, so the pronoun must be mér.

Compare:

• mig = accusative me
• mér = dative me

So:

• með mér = with me

This is very common in Icelandic: prepositions often require a specific case.

Yes, very much so.

Taka eitthvað með sér means to take something with oneself / take something along.

In the sentence, the subject is ég, so sér becomes mér:

• ég tek ... með mér = I take ... with me
• hann tekur ... með sér = he takes ... with him

So the phrase is not just random word-by-word assembly; it is a very normal Icelandic pattern.

Icelandic usually uses í when talking about being inside a vehicle.

So:

• í strætó = on the bus / in the bus

English prefers on the bus, but Icelandic conceptualizes it more as inside the bus.

Also, if you wanted to mean by bus as a method of transport, Icelandic often uses með strætó instead.

That is a good thing to notice.

Here, í means location, so it would normally go with the dative. But strætó often keeps the same visible form, so you do not see an obvious ending change.

So even though the grammar is doing case work, the noun itself does not look different here.

Á morgnana means in the mornings or every morning.

The plural is important because it gives a habitual sense: this is something that happens regularly, not just once.

So:

• á morgnana = in the mornings
• not just one specific morning

This is a very common Icelandic time expression.

Because á morgnana is a fixed time expression in Icelandic.

You should learn it as a set phrase meaning:

• in the mornings
• every morning

It does not translate word-for-word in a neat way from English, so it is best to memorize it as a natural Icelandic expression.

Useful contrasts:

• í morgun = this morning
• á morgun = tomorrow
• á morgnana = in the mornings

Yes. Icelandic word order is fairly flexible, although not completely free.

This sentence has a neutral order:

• Ég tek heyrnartólin með mér í strætó á morgnana.

But you could move the time phrase to the front for emphasis:

• Á morgnana tek ég heyrnartólin með mér í strætó.

Notice that when something other than the subject comes first, the finite verb still stays in the second position. That is an important Icelandic pattern.