Mér er illt í olnboganum eftir vinnu.

Because Icelandic often expresses physical discomfort with an impersonal construction.

• mér = to me / for me (dative of ég)
• er = is
• illt = painful / bad / sore

So Mér er illt is literally something like To me it is painful.

In English, we usually say I have pain or my elbow hurts, but Icelandic often uses this different pattern. So ég er illt would not be correct here.

As a chunk, mér er illt means I am in pain, it hurts, or I feel sore/painful.

It is a very common Icelandic way to talk about pain or discomfort. The body part can then be added with í:

• Mér er illt í bakinu = My back hurts
• Mér er illt í höfðinu = I have a headache / My head hurts
• Mér er illt í olnboganum = My elbow hurts

So it is best to learn mér er illt as a useful expression, not just word by word.

Illt is the neuter singular form of the adjective illur.

In this kind of impersonal expression, Icelandic normally uses the neuter singular predicate form, even though there is no normal nominative subject like hann, hún, or það referring to a thing.

So:

• illur = masculine
• ill = feminine
• illt = neuter

Here, the language uses illt by default.

It is also important not to confuse illt with illa:

• illt = adjective form used here
• illa = adverb, meaning badly

So Mér er illt is correct, not Mér er illa for this meaning.

Because Icelandic says that the pain is in the body part:

• í = in
• olnboganum = the elbow in the dative singular

So í olnboganum literally means in the elbow.

This is the normal Icelandic way to locate pain in a body part. English often prefers my elbow hurts, but Icelandic often uses it is painful in the elbow.

Because the preposition í can take either:

• accusative for motion into something
• dative for location in something

Here there is no movement. The pain is located in the elbow, so Icelandic uses the dative.

That is why you get:

• dictionary form: olnbogi = elbow
• dative singular definite: olnboganum = in the elbow / the elbow

This is a very common pattern with í.

The ending shows both case and definiteness.

olnboganum breaks down like this:

• olnboga- = stem
• -num = dative singular definite ending

So it means the elbow in the dative singular.

Compare:

• olnbogi = an elbow / elbow (nominative singular)
• olnbogann = the elbow (accusative singular)
• olnboganum = the elbow (dative singular)

A learner does not need to memorize every form immediately, but it is useful to notice that the ending changes because of grammar, not because it is a different word.

In Icelandic, body parts are very often expressed with the definite article rather than a possessive, especially when the owner is already clear from the sentence.

Here, mér already tells you whose elbow is involved: my elbow.

So Icelandic naturally says:

• Mér er illt í olnboganum
  literally: It is painful to me in the elbow

Instead of something more explicit like mínum olnboga. That kind of possessive wording is possible in some contexts, but it is usually less natural here.

This is similar to how some European languages say things like the head hurts to me rather than my head hurts.

Eftir vinnu means after work.

Here:

• eftir = after
• vinnu = accusative singular of vinna (work)

The preposition eftir takes the accusative, so vinna becomes vinnu.

It also usually appears without the article here because it means work in a general sense:

• eftir vinnu = after work
• not necessarily after the work

This is very similar to English expressions like after school, at home, or after dinner, where no article is needed in many contexts.

Yes, you may hear both illt and sárt, but they are not always identical in feel.

Very roughly:

• illt often means painful / sore / aching
• sárt often suggests painful / hurting, and can sometimes feel a bit more like a sharp or tender pain

In many everyday situations, both can work. But the exact choice depends on nuance, context, and speaker preference.

Other common ways to express the same general idea are:

• Ég er með verki í olnboganum = I have pain in my elbow
• Olnboginn á mér er aumur = My elbow is sore/tender

So the sentence you were given is natural, but it is not the only possible wording.

The given order is natural, but Icelandic word order can be somewhat flexible.

Normal version:

• Mér er illt í olnboganum eftir vinnu.

You could also move the time phrase for emphasis:

• Eftir vinnu er mér illt í olnboganum.

That might sound more like After work, my elbow hurts.

What matters most is keeping the grammatical relationships clear:

• mér stays dative
• illt stays neuter singular
• í olnboganum stays the location of the pain
• eftir vinnu stays the time phrase

So yes, the order can change, but the original sentence is a very good neutral model to learn.

Usually eftir vinnu means after work in a broad everyday sense:

• after work
• after my workday
• after a work shift
• after being at work

It does not have to refer to a specific piece of work. It is more like the routine activity or period of working.

If you wanted to be more specific, Icelandic could do that too, but eftir vinnu is the normal everyday phrase for after work.