Selidba je bila toliko naporna da smo odmah zaspali.

Selidba is in the nominative singular because it is the subject of the sentence.

• selidba = the move / moving house
• je bila = was

So Selidba je bila... literally means The move was...

The noun selidba is a feminine noun, which matters for the adjective later: naporna.

Because naporna has to agree with selidba.

In Croatian, adjectives agree with the noun in:

• gender
• number
• case

Here:

• selidba is feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• masculine: naporan
• feminine: naporna
• neuter: naporno

That is why the sentence has naporna.

Toliko ... da means so ... that.

So:

• toliko naporna = so exhausting
• da smo odmah zaspali = that we fell asleep immediately

This is a very common structure in Croatian:

• Bio je toliko umoran da nije mogao raditi.
  = He was so tired that he couldn’t work.
• Bilo je toliko hladno da nismo izašli.
  = It was so cold that we didn’t go out.

So in your sentence, toliko strengthens the adjective and da introduces the result.

Sometimes learners wonder about this because both can relate to so in English.

In this sentence, toliko naporna da... is the most natural choice for so exhausting that...

Very roughly:

• tako often means like this / like that / so
• toliko often means that much / so much / to such an extent

Before an adjective in a result clause with da, toliko is very common and natural:

• toliko umoran da... = so tired that...
• toliko gladan da... = so hungry that...

You may also hear tako naporna da..., and it can work in some contexts, but toliko is a very standard choice here because it emphasizes degree.

Both are possible.

Croatian word order is fairly flexible, but there are rules about clitics like je and smo, which usually come early in the clause.

Here the sentence has:

• da smo odmah zaspali

This is a normal and natural order after da.

You can also hear:

• da smo zaspali odmah
• sometimes da zaspali smo is not correct, because smo cannot just go anywhere

So the important point is that smo is a clitic and usually appears near the beginning of its clause.

It is the past tense.

Croatian past tense is usually formed with:

• the present of biti (to be) as an auxiliary
• plus the l-participle

Here:

• smo = we are as an auxiliary form used in the past tense
• zaspali = past participle of zaspati (to fall asleep)

So:

• mi smo zaspali = we fell asleep / we have fallen asleep

In Croatian, this same form can often cover what English expresses as either simple past or present perfect, depending on context.

Because zaspati and spavati mean different things.

• spavati = to sleep
• zaspati = to fall asleep

Your sentence is about the moment they went from being awake to asleep, so zaspati is the right verb.

Compare:

• Spavali smo. = We were sleeping / We slept.
• Zaspali smo. = We fell asleep.

So odmah zaspali means fell asleep immediately, not just slept immediately.

Yes, zaspati is a perfective verb.

Croatian verbs often come in aspect pairs:

• spavati = imperfective
• zaspati = perfective

A perfective verb presents the action as a completed whole or as a single event. That fits perfectly here, because the sentence describes the result of the exhausting move:

• the move was exhausting
• as a result, we fell asleep

If you used spavati, the focus would be on the state or process of sleeping, not the moment of falling asleep.

Odmah means immediately / right away.

In this sentence:

• da smo odmah zaspali = that we fell asleep immediately

Its position is quite natural here, before the main verb idea zaspali.

Croatian adverbs like odmah can move around somewhat:

• Odmah smo zaspali.
• Smo odmah zaspali is not possible on its own because of clitic rules
• Zaspali smo odmah.

These can all be grammatical depending on context, but smo odmah zaspali is a very normal order.

Da introduces the subordinate clause expressing the result.

In English, you say:

• so exhausting that we fell asleep

In Croatian, the equivalent is:

• toliko naporna da smo odmah zaspali

So da here means that in the sense of a result clause, not the yes word in some other Slavic languages.

It connects the first idea and the consequence:

• Selidba je bila toliko naporna
• da smo odmah zaspali

Yes, that is a very close literal translation.

Piece by piece:

• Selidba = the move
• je bila = was
• toliko naporna = so exhausting
• da = that
• smo = auxiliary for we
• odmah = immediately
• zaspali = fell asleep

A very literal translation is:

The move was so exhausting that we immediately fell asleep.

A more natural English version might also be:

The move was so exhausting that we fell asleep right away.

Yes, you could say:

Selidba je bila toliko naporna da smo mi odmah zaspali.

But usually mi is not needed, because smo already tells you the subject is we.

Adding mi gives extra emphasis or contrast, for example:

• ...da smo mi odmah zaspali, a oni nisu.
  = ...that we fell asleep immediately, but they didn’t.

So in the original sentence, leaving out mi is completely normal.

Yes, it is fully natural and standard.

It uses very common grammar:

• past tense with je bila
• adjective agreement: naporna
• the result pattern toliko ... da
• a natural past form smo zaspali

So this is a good model sentence for everyday Croatian.