De bjöd in oss förra helgen, så nu vill vi bjuda in dem hem till oss i sommar.

Because bjuda is an irregular verb.

Its main forms are:

• bjuda — infinitive
• bjöd — past tense
• bjudit — supine/past participle base

So De bjöd in oss means They invited us.

This is something you mostly have to learn as a verb pattern, much like irregular verbs in English.

Because bjuda in is a particle verb.

In Swedish, particle verbs often split when the verb is finite in a main clause:

• De bjöd in oss
• Vi bjuder in dem

But when the verb is in the infinitive, the verb and particle usually stay together:

• vill bjuda in dem

So:

• bjöd in = past-tense finite verb + particle
• bjuda in = infinitive + particle

Because vill is a modal verb, and modal verbs are normally followed directly by the infinitive.

So you say:

• vill bjuda in
• kan komma
• ska gå
• måste åka

Not:

• vill att bjuda in

That would sound wrong in Swedish.

Because Swedish distinguishes between subject and object forms in writing.

• de = they, subject form
• dem = them, object form

So:

• De bjöd in oss = They invited us
• vi vill bjuda in dem = we want to invite them

A useful shortcut:

• the person doing the action → de
• the person receiving the action → dem

In everyday speech, both are very often pronounced dom.

For the same reason as dem above: oss is the object form of vi.

• vi = we
• oss = us

After a verb like bjuda in, you need the object form:

• bjuda in oss
• bjuda in mig
• bjuda in henne
• bjuda in dem

So De bjöd in oss is correct, not De bjöd in vi.

Because Swedish often uses time expressions without a preposition.

So you say:

• förra helgen = last weekend
• förra veckan = last week
• förra året = last year
• nästa måndag = next Monday

English often needs a preposition in some time expressions, but Swedish often does not.

So De bjöd in oss förra helgen is completely normal.

Hem means home or homeward, and till oss means to us / to our place.

Together, hem till oss means something like:

• to our home
• over to our place

Why both?

• hem gives the idea of going to someone’s home
• till oss tells you whose home it is

So bjuda in dem hem till oss means inviting them to come to our place.

It is understandable and grammatically fine, but many Swedes would very often say bjuda hem dem instead when the invitation is to your home.

For example:

• Nu vill vi bjuda hem dem i sommar

That can sound more idiomatic.

Very roughly:

• bjuda in = invite
• bjuda hem = invite over / invite to one’s home

So the sentence you have is correct, but bjuda hem is worth learning as a very common alternative.

Because Swedish often does not use a separate future tense the way some languages do.

Future meaning is often shown by:

• the present tense + a time expression
• ska
• kommer att
• a verb like vill, depending on the meaning

Here, vill means want to right now, and i sommar gives the future time.

So the structure is basically:

• now we want
• to invite them
• this summer

The sentence is not mainly about future grammar; it is about present desire/intention.

Because så here means so, connecting the second main clause to the first one.

After that, nu is placed before the finite verb to give the sense of so now...

Swedish main clauses normally follow the verb-second pattern, meaning the finite verb comes in the second position:

• Nu vill vi bjuda in dem
• I sommar vill vi bjuda in dem

In så nu vill vi, the clause after så is still a normal main clause, and vill stays in second position within that clause.

Yes. That would also be natural.

• Nu vill vi bjuda in dem hem till oss i sommar

Adding så makes the connection to the first clause clearer:

• They invited us last weekend, so now...

Without så, the sentence still works, but the cause-and-result link is a little less explicit.

In everyday spoken Swedish, both are very commonly pronounced dom.

So although the sentence is written:

• De bjöd in oss ... bjuda in dem ...

many speakers would say something close to:

• Dom bjöd in oss ... bjuda in dom ...

This is very useful to know, because learners often get confused when the written forms and spoken forms do not match exactly.