Skjorten er rynkete, så jeg må stryke den.

Because Norwegian usually marks the definite form by adding an ending to the noun.

• skjorte = shirt / a shirt
• skjorten = the shirt

So -en here is the definite singular ending. Unlike English, Norwegian often puts the idea at the end of the noun instead of using a separate word.

Den means it and refers back to skjorten.

Since skjorte is a common gender noun, the pronoun is den:

• skjorten → den

If the noun were neuter, you would usually use det instead.

You could also say:

• Skjorten er rynkete, så jeg må stryke skjorten.

But using den sounds more natural because it avoids repeating the noun.

Because må is a modal verb, and modal verbs in Norwegian are followed by the bare infinitive.

So you say:

• jeg må stryke
• jeg kan stryke
• jeg vil stryke

Not:

• jeg må å stryke

This is similar to English:

• I must iron
• not I must to iron

Rynkete is an adjective describing the shirt.

In this sentence it comes after er, so it is being used predicatively:

• Skjorten er rynkete. = The shirt is wrinkled.

That is different from using it directly before the noun:

• en rynkete skjorte = a wrinkled shirt

The form rynkete is just the normal adjective form used here.

Here så means so, and it is joining two main clauses:

• Skjorten er rynkete
• så jeg må stryke den

After this kind of så, Norwegian keeps normal main-clause word order:

• subject + verb → jeg må

So så jeg må ... is the natural order here.

If you said så må jeg ..., it could sound more like then I have to... or give a slightly different emphasis.

Here så means so / therefore / as a result.

It connects the two ideas:

• the shirt is wrinkled
• as a result, I have to iron it

So in this sentence, så is not the adverb meaning so as in so big. It is a conjunction linking cause and result.

Because skjorte is not a neuter noun.

In Norwegian, third-person pronouns for things usually match grammatical gender:

• common gender noun → den
• neuter noun → det

So:

• skjorten → den

If the sentence were about huset (the house), you would say:

• Huset er gammelt, så jeg må male det.

Yes, in Bokmål it can be treated as feminine by speakers who use feminine forms.

That means you may see:

• ei skjorte / skjorta

But many speakers use the common-gender forms:

• en skjorte / skjorten

So the sentence with skjorten is completely normal. Norwegian Bokmål often allows both systems, depending on the speaker’s style.

Only if you want past tense.

• må = must / have to in the present
• måtte = had to in the past

So:

• Skjorten er rynkete, så jeg må stryke den. = present situation
• Skjorten var rynkete, så jeg måtte stryke den. = past situation

Yes. Both are grammatically correct.

• Skjorten er rynkete, så jeg må stryke den.
• Skjorten er rynkete, så jeg må stryke skjorten.

But using den is usually more natural because the shirt has just been mentioned. Repeating skjorten is possible, but slightly less elegant unless you want extra emphasis or clarity.