Ordren bliver forsinket, fordi varen er udsolgt.

Because Danish usually puts the definite article on the end of the noun.

• ordre = order
• ordren = the order
• vare = item / product / goods
• varen = the item / the product

This is one of the biggest differences from English. Instead of a separate word like the, Danish often uses a suffix:

• en vare = an item
• varen = the item

Bliver forsinket is a passive construction.

It is made from:

• bliver = present tense of blive (become / get / be in passive constructions)
• forsinket = past participle of forsinke (delay)

So ordren bliver forsinket literally means something like the order gets delayed or the order is being delayed, but in natural English it is often just the order is delayed.

This blive + past participle pattern is very common in Danish for expressing the passive.

Both can be possible, but they are not exactly the same.

• bliver forsinket focuses more on the event or process: the order gets / is being delayed
• er forsinket focuses more on the resulting state: the order is delayed

In many real-life contexts, the difference is small, but bliver forsinket often sounds like something is causing the delay right now, which fits well with because the item is sold out.

Yes. That is another passive form in Danish.

So you could say:

• Ordren bliver forsinket
• Ordren forsinkes

Both mean roughly the order is delayed.

The difference is mainly style:

• bliver forsinket is very common and often feels a bit more everyday and explicit
• forsinkes is a shorter passive form and can sound slightly more formal or administrative

In messages from shops or companies, both are possible.

Vare is a broad word. It can mean:

• item
• product
• goods
• merchandise

In this sentence, varen most naturally means the item or the product that was ordered.

So it does not have to mean a general kind of goods; here it probably refers to the specific product in the order.

Udsolgt means sold out.

It is built from:

• ud = out
• solgt = sold (from sælge, to sell)

So it is very similar to English in structure: sold out.

In the sentence varen er udsolgt, udsolgt works like an adjective describing the status of the item.

Other examples:

• Produktet er udsolgt = The product is sold out
• De er udsolgte = They are sold out

Because Danish often attaches the definite article directly to the noun instead of using a separate word.

So:

• ordren already means the order
• varen already means the item

English uses the order. Danish often uses just one word: ordren.

A separate definite word can appear in Danish too, but usually with adjectives or certain other structures, for example:

• den forsinkede ordre = the delayed order

Here you get both:

• den = separate definite marker
• ordre = noun
• plus the adjective form

But in your sentence, there is no adjective before the noun, so the simple suffixed form is used.

Because fordi introduces a subordinate clause, and Danish normally uses a comma before such clauses in standard writing.

So the sentence is divided into:

• main clause: Ordren bliver forsinket
• subordinate clause: fordi varen er udsolgt

That is why the comma appears before fordi.

This is very normal in written Danish.

Yes, fordi introduces a subordinate clause, and subordinate clauses in Danish can show different word order from main clauses, especially when adverbs are present.

In your sentence:

• fordi varen er udsolgt

the order looks straightforward because there is no adverb like ikke.

But compare:

• main clause: Varen er ikke udsolgt
• subordinate clause: fordi varen ikke er udsolgt

Notice that in the subordinate clause, ikke comes before the finite verb er.

So even though your example does not make the difference very obvious, fordi is still introducing a subordinate clause.

Because er udsolgt describes the current status: the item is sold out.

• er udsolgt = it is in a sold-out state
• bliver udsolgt = it becomes sold out / sells out

So:

• Varen er udsolgt means the item is already unavailable now
• Varen bliver udsolgt would mean the item is selling out or becoming unavailable

In your sentence, the reason for the delay is the item's current status, so er udsolgt is the natural choice.