Hvis min skjorte ikke havde ligget så længe i tasken, ville jeg ikke have strøget den i går aftes.

It is a past unreal / counterfactual conditional.

The pattern is:

• Hvis
  • past perfect: hvis min skjorte ikke havde ligget ...
• ville
  • have
    • past participle: ville jeg ikke have strøget den ...

This tells us the speaker is imagining a different past situation and a different past result. In other words, the shirt did lie in the bag for a long time, and the speaker did iron it last night.

Because Danish usually uses the past perfect in the hvis-clause for an unreal past condition.

• havde ligget = had been lying / had lain
• lå = lay / was lying

If you said Hvis min skjorte ikke lå så længe i tasken, it would not match this past counterfactual meaning very well. The form havde ligget clearly signals that the speaker is talking about an imagined change to an earlier past situation.

Ligge is very natural for objects that are physically somewhere, especially when they are left somewhere for a while.

So:

• skjorten havde ligget i tasken = the shirt had been lying / had been sitting in the bag
• skjorten havde været i tasken = the shirt had been in the bag

Both are possible, but ligget is a bit more concrete and physical. It helps you picture the shirt being crumpled or left there.

Because Danish main clauses follow the V2 rule: the finite verb must come in the second position.

Here, the whole hvis-clause comes first:

• Hvis min skjorte ikke havde ligget så længe i tasken = position 1

So the main clause must begin with the finite verb:

• ville = position 2
• jeg = comes after it

That is why you get:

• Hvis ..., ville jeg ...

and not:

• Hvis ..., jeg ville ...

This is a very common word-order question.

In a subordinate clause like the hvis-clause, Danish usually has:

• subject + sentence adverb + finite verb

So:

• min skjorte = subject
• ikke = sentence adverb
• havde = finite verb

That gives:

• Hvis min skjorte ikke havde ligget ...

In the main clause, because of V2 word order, the finite verb comes before the subject here:

• ville = finite verb
• jeg = subject
• ikke = sentence adverb

So:

• ville jeg ikke have strøget den

Here så længe means so long or for such a long time.

So:

• ikke havde ligget så længe i tasken = had not been lying in the bag for so long

Danish often uses så længe very naturally in this kind of sentence. You could also say something like i så lang tid, but så længe is idiomatic and simple.

Strøget is the past participle of stryge, which here means to iron.

Its main forms are:

• infinitive: stryge
• past tense: strøg
• past participle: strøget

So:

• jeg strøg skjorten = I ironed the shirt
• jeg har strøget skjorten = I have ironed the shirt
• jeg ville have strøget skjorten = I would have ironed the shirt

Because Danish forms the conditional perfect with:

• ville
  • have
    • past participle

So:

• ville have strøget = would have ironed

This is the normal way to talk about an unreal result in the past.

Compare:

• jeg ville stryge den = I would iron it
• jeg ville have strøget den = I would have ironed it

The second one points to a past result that did not happen.

Because skjorte is a common-gender noun in Danish, and the normal pronoun for a common-gender noun is den.

So:

• en skjorte
• skjorten
• den

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

Because tasken means the bag, and that can be enough if the bag is already understood from context.

So the sentence does not necessarily mean the shirt was in someone else’s bag. It just means in the bag, where the specific bag is assumed to be known or irrelevant.

If you wanted to make the ownership explicit, you could absolutely say:

• Hvis min skjorte ikke havde ligget så længe i min taske ...

That would be perfectly natural too.

I går aftes means last night or more literally yesterday evening.

It refers to the evening of the previous day.

A closely related expression is i aftes, which also commonly means last night. I går aftes is just more explicit.

Not directly. The idea is that the shirt being in the bag for a long time probably made it wrinkled, and that is why the speaker ironed it.

So the logic is:

• it lay in the bag for a long time
• therefore it got creased
• therefore the speaker ironed it

Danish often leaves that middle step understood rather than stated outright.

Yes. That is a very close literal match.

But for natural English, many speakers would prefer something like:

• If my shirt hadn’t been in the bag so long, I wouldn’t have ironed it last night.
• If my shirt hadn’t been lying in the bag so long, I wouldn’t have ironed it last night.

So the Danish structure corresponds quite closely to English, but English often smooths ligget into been in ordinary speech.