Jeg er trøtt, men jeg må likevel gå til jobb.

Likevel means nevertheless, still, or even so.

In this sentence, it shows contrast:

• Jeg er trøtt = I am tired
• men jeg må likevel gå til jobb = but I still / nevertheless have to go to work

So likevel adds the idea despite being tired.

Because men joins two separate clauses, and each clause normally needs its own subject and verb.

The two clauses are:

• Jeg er trøtt
• jeg må likevel gå til jobb

In English, we do the same:

• I am tired, but I still have to go to work.

So repeating jeg is completely normal and necessary.

In Norwegian, states like tired, happy, sad, and ready are usually expressed with to be + adjective.

So:

• Jeg er trøtt = I am tired
• Hun er glad = She is happy
• Vi er klare = We are ready

English works the same way here, so this part is quite straightforward.

Må is the present tense of måtte, and here it means must or have to.

So:

• jeg må gå = I must go / I have to go

It usually expresses:

• obligation
• necessity
• something the speaker feels is required

In everyday English, have to is often the most natural translation, even though must is also correct.

Because må is a modal verb, and after modal verbs in Norwegian, the next verb normally comes in the bare infinitive form, without å.

So:

• jeg må gå = I have to go
• jeg kan komme = I can come
• jeg vil spise = I want to eat
• jeg skal jobbe = I am going to work / I will work

Compare that with a non-modal verb:

• Jeg liker å gå = I like to walk / go

So the absence of å after må is normal grammar.

In a normal Norwegian main clause, the finite verb usually comes early, and adverbs like likevel often come after it.

So:

• jeg må likevel gå til jobb

This is very natural word order.

You can also move likevel for emphasis:

• Likevel må jeg gå til jobb. = Nevertheless, I have to go to work.

Both are correct, but the original sentence sounds very natural and neutral.

Because til shows movement toward a destination.

• gå til jobb = go to work
• dra til jobb = go to work
• komme til jobb = get to work

By contrast, på jobb means at work:

• Jeg er på jobb. = I am at work.

So:

• til jobb = destination
• på jobb = location/state

Because jobb is often used without an article in fixed expressions meaning work in a general sense.

For example:

• gå til jobb = go to work
• være på jobb = be at work
• dra på jobb = go to work

This is similar to English, where we also usually say go to work, not go to the work.

If you were talking about a specific job or workplace in a more concrete way, the wording could be different, but in this sentence the article is naturally omitted.

Because jeg is singular, and the adjective is in the singular form.

Here:

• Jeg er trøtt. = I am tired.

With a plural subject, you would use trøtte:

• Vi er trøtte. = We are tired.
• De er trøtte. = They are tired.

So the sentence uses the correct form for a singular subject.

Yes, this comma is standard and expected here because men connects two full clauses:

• Jeg er trøtt
• jeg må likevel gå til jobb

Since both parts have their own subject and verb, the comma is normally used:

• Jeg er trøtt, men jeg må likevel gå til jobb.

So the punctuation in the sentence is correct.