Efter opvasken slapper jeg af på sofaen i stuen.

I

Breakdown of Efter opvasken slapper jeg af på sofaen i stuen.

• i: in
• på: on
• stuen: the living room

Questions & Answers about Efter opvasken slapper jeg af på sofaen i stuen.

Why does the sentence start with Efter opvasken—does that change word order?

Yes. When something other than the subject comes first in a main clause, Danish uses V2 word order: the finite verb must be in the second position.
So with Efter opvasken first, you get:

• Efter opvasken (fronted element) + slapper (finite verb) + jeg (subject) + af … If you start with the subject instead, it’s:
• Jeg slapper af på sofaen i stuen efter opvasken.

What exactly is opvasken grammatically?

Opvasken is opvask (washing up / the dishes) + the definite suffix -en, so it means the washing up / the dishwashing.
Danish often makes nouns definite by attaching -en/-et rather than using a separate word like the.

Why is it Efter opvasken and not something like Efter den opvask?

Because Danish commonly uses the definite noun form when English would say after the washing up.
You can say efter den opvask, but that tends to sound more specific/pointing, like after that washing up (emphasizing a particular one).

Is opvask a noun or a verb here, and could you say it differently?