Med en gang klesbyttemarkedet åpner, starter vi bytterunden.

Here, med en gang means as soon as.

So:

• Med en gang klesbyttemarkedet åpner = As soon as the clothes-swap market opens

A useful thing to know is that med en gang can also mean immediately / right away in other contexts.
For example:

• Kom hit med en gang! = Come here right away!

So the exact meaning depends on the sentence.

This is because Norwegian follows the V2 rule in main clauses: the finite verb usually comes in the second position.

In this sentence, the first position is taken by the whole time clause:

• Med en gang klesbyttemarkedet åpner

So the main clause must begin with the verb:

• starter vi bytterunden

That is why you get:

• Med en gang klesbyttemarkedet åpner, starter vi bytterunden.

If you start with the subject instead, then you would say:

• Vi starter bytterunden med en gang klesbyttemarkedet åpner.

Both are correct; the difference is mainly emphasis and sentence structure.

Norwegian very often uses the present tense for future events, especially when the event is:

• planned
• scheduled
• expected from the context

So:

• klesbyttemarkedet åpner literally looks like the clothes-swap market opens
• but in context it can mean when the clothes-swap market opens / when it opens later

Likewise:

• Vi starter vi bytterunden = We start the swapping round
• but naturally in English you might translate it as we’ll start the swapping round

This is very normal in Norwegian.

It is a compound noun, which is extremely common in Norwegian.

It can be broken down like this:

• klær / kles- = clothes
• bytte = exchange / swap
• marked = market
• -et = the definite ending for a neuter noun

So:

• klesbyttemarkedet = the clothes-swap market

A very important Norwegian pattern is that in a compound noun, the definite ending usually goes only on the last part.

Compare:

• et marked = a market
• markedet = the market

So the whole compound becomes definite by making the last element definite.

In compounds, Norwegian often uses a special stem or linking form rather than the full standalone word.

The normal noun is:

• klær = clothes

But in compounds, you often see:

• klesbutikk = clothing store
• kleshenger = clothes hanger
• klesbytte = clothes swap

So kles- is just the normal compound form here.

This is something learners mostly have to get used to by exposure, because compound forms are not always fully predictable from the standalone noun.

Bytterunden is also a compound noun:

• bytte = swap / exchange
• runde = round
• -n = the definite ending

So:

• en bytterunde = a swapping round / a round of exchanging
• bytterunden = the swapping round

In this context, it suggests a specific stage or round in the event when people actually start swapping items.

The comma separates the subordinate clause from the main clause.

Structure:

• Med en gang klesbyttemarkedet åpner = subordinate clause
• starter vi bytterunden = main clause

In Norwegian, it is common to use a comma after an introductory subordinate clause like this, especially in written language.

So the comma helps show the boundary between:

1. the time clause
2. the main statement

It is not exactly “at the end” because it is simply following the subject in a subordinate clause.

Inside the subordinate clause:

• klesbyttemarkedet = subject
• åpner = finite verb

So the order is:

• Med en gang + subject + verb

This is normal Norwegian subordinate-clause word order.

The more noticeable word-order feature in this sentence is really in the main clause:

• starter vi instead of
• vi starter

because the subordinate clause has taken first position.

Yes, that would also be correct.

The difference is mainly one of nuance:

• Når = when
• Med en gang = as soon as / immediately when

So med en gang gives a stronger sense of immediacy. It emphasizes that the swapping round begins right after the market opens, with no delay.

Yes. A very natural alternative is:

• Vi starter bytterunden med en gang klesbyttemarkedet åpner.

This means the same thing.

The difference is emphasis:

• Med en gang klesbyttemarkedet åpner, starter vi bytterunden.
  This puts the time condition first and gives it more prominence.

• Vi starter bytterunden med en gang klesbyttemarkedet åpner.
  This starts with we, which can sound slightly more neutral in some contexts.

It is neutral and natural Norwegian.

Nothing in the sentence is especially formal or especially casual. It would fit well in:

• event announcements
• instructions
• schedules
• spoken explanations

The compound nouns are a bit long, but that is completely normal in Norwegian, especially in practical or organizational contexts.