Can anyone recommend a van/shuttle service for a family of 7 from Arlanda airport to our Airbnb in Stockholm?
Where are you staying?
Near Lumaparken (Luma Park).
That was a bit of an odd choice, any particular reason for staying there? But in this case first take the train to Stockholm's central station. From there you can either take a taxi to Lumaparken or metro+tram or tram+boat.
You can of course take a taxi from the airport to Lumaparken, but the train will save you both time and money.