Ég teygi mig í smástund eftir vinnu.

A word-for-word breakdown is:

Ég = I
teygi = stretch / am stretching
mig = myself / me
í smástund = for a short while
eftir vinnu = after work

So the whole sentence means I stretch for a little while after work.

Because teygja sig is the usual reflexive expression for to stretch oneself.

So:

Ég teygi mig = I stretch / literally I stretch myself

If you leave out mig, the verb teygja more easily sounds like you are stretching something else, extending something, or pulling something out.

For an English speaker, this is a good pattern to remember:

• teygja sig = stretch oneself
• setja sig = sit down
• hreyfa sig = move oneself

Because sig is the reflexive form used for the third person.

So:

• Ég teygi mig = I stretch myself
• Þú teygir þig = you stretch yourself
• Hann/Hún teygir sig = he/she stretches himself/herself

A common learner mistake is trying to use sig for every person, but Icelandic does not do that.

Teygi is the 1st person singular present tense of teygja.

So the pattern is:

• ég teygi = I stretch
• þú teygir = you stretch
• hann/hún teygir = he/she stretches

As a standalone sentence, the present tense here often sounds habitual:
I stretch for a little while after work.

But depending on context, it can also describe what is happening right now.

Here í smástund means for a short while, not in a short while.

This is an important difference from English. In Icelandic, í is often used with expressions of duration:

• í smástund = for a short while
• í tvo daga = for two days
• í nokkrar mínútur = for a few minutes

So in this sentence, í smástund tells you how long the stretching lasts.

If you wanted in a moment / soon, you would use something else, such as bráðum or eftir smástund, depending on the exact meaning.

Yes, smástund is normally written as one word here. Icelandic often likes compounds.

In this sentence it is in the accusative singular because í is being used in a duration expression.

The useful thing to notice is that even though it is accusative, the form smástund looks the same as the nominative here.

So the grammar is:

í + accusative for duration
→ í smástund

Vinnu is dative singular of vinna.

The preposition eftir here means after, and in this use it takes the dative:

• eftir vinnu = after work
• eftir skóla = after school
• eftir mat = after food / after the meal

So this is a preposition-and-case combination you should learn as a set: eftir + dative

Without the article, eftir vinnu means after work in a general sense, much like English.

With the article, eftir vinnuna would mean something more like:

• after the work
• after the shift
• after the job/task we are talking about

So the difference is roughly:

• eftir vinnu = after work, generally
• eftir vinnuna = after the work / after the shift, more specific

In your sentence, the article is omitted because the idea is general and routine.

Yes. Icelandic word order is flexible, but it still follows the verb-second pattern in main clauses.

Your sentence: Ég teygi mig í smástund eftir vinnu.

A very natural alternative: Eftir vinnu teygi ég mig í smástund.

Notice what happened:

• Eftir vinnu moved to the front
• the verb teygi stayed in second position
• ég moved after the verb

So you can move parts around for emphasis, but you cannot simply keep English-style word order.

Yes, it is natural.

A few nearby alternatives are:

• Ég teygi mig aðeins eftir vinnu.
  = I stretch a little after work.

• Ég geri teygjur eftir vinnu.
  = I do some stretches after work.

• Eftir vinnu teygi ég mig í smástund.
  = After work, I stretch for a little while.

The version with teygi mig focuses on stretching myself.
The version with geri teygjur sounds a bit more like doing stretching exercises.

A rough English-friendly guide is:

Ég ≈ yeg
teygi ≈ TAY-yi
mig ≈ mihgh with a soft throaty ending
í ≈ ee
smástund ≈ SMAU-stund
eftir ≈ EF-tir
vinnu ≈ VIN-nu

So the whole sentence is roughly:

yeg TAY-yi mihgh ee SMAU-stund EF-tir VIN-nu

A few pronunciation notes:

• ey sounds like the vowel in day
• á sounds like ow in now
• the final g in Ég and mig is not a hard English g

If you want to sound natural, the biggest things to focus on are:

1. ey in teygi
2. á in smástund
3. the soft ending of Ég and mig