Asker Transportation

Getting to Asker by aeroplane isn't really an option, but close:
At Oslo Gardermoen Airport (OSL), take the Airport Exress train to Asker. Every second departure goes to Asker, the end of the line for the Airport Express. It takes 50 minutes from the airport.
The cost: Oslo-Asker by Airport Express train is 190 NOK if you use a card machine, NOK 200 if paying cash, the regular train options are cheaper, but crowded during rush hours and a dearth of lugage space. Somewhat slower, too, but that's not so much of an argument.
The cheaper option is thus to take the regular through trains to/from the airport on the Larvik/Skien - Lillehammer route. By other trains than these you will need to change at Oslo Central station.
Getting to Asker from Torp airport/Sandefjord is probably best by the Torp-Oslo airport bus - it will stop at Asker bus/railway station if you ask. But you can also hop on the train via the NSB shuttle to Torp Station from the Torp Airport.
Note that there is not an airport bus service from Asker to OSL. The nearest airport bus stop is Bekkestua in Bærum municipality, so if in eastern Asker it makes sense to get on there.

AS Nesodden-Bundefjord Dampskibsselskap can assist you in takeing care of odd shipping orders, whether cargo or passengers. They do regular passenger shipping on the Oslo Fjord, but can do a host of other maritime-related things, too.

During summers you can catch the boats from Aker Brygge (Oslo), route No 256 to Vollen and Slemmestad, and route 711 Sandvika - Vestfjord islands to Holmen Quay.

The first one has been awarded another VT Asker transportation tip, the second is a summer weekends-only recreational route that visits islands and drops and pick up people cantering between the islands. They run Friday-Sundays from about 20th June to about 20th August. If you miss your boat you may have to swim or if on the mainland... catch a bus or a local train back to Oslo - or Asker. Details for the season available at Trafikanten.

Boats named Rigmor and Rigfar run route 711 Sandvika-Holmen with drop-off/pick up points at Borøya, Brønnøya, Ostøya and Langåra islands.

There are frequent train connections between Asker and Oslo. You can basically go to the station and expect that within half an hour there will be a train. However, late at night the frequency is more limited so check out your options beforehand.

Asker train station has recently been renewed and refurbished. It is now a practical station with easy access by bus, foot, taxi and car.
The station is located at the convergence of the Moss-Spikkestad line, the Kongsberg-Eidsvoll line, Drammen-Ås suburban line, Lillehammer-Skine line, Oslo-Bergen and Oslo-Stavanger lines. The airport Express train departs from track no 5.
The stations is well integrated with bus and taxi stations.
There is an underpass with esoteric lighting and music arts, and a steep inconvenient overpass to the tracks.
The station ticket offices close early and generally expect limited services from here. Board trains directly if it is closed.

Amsterdam-Asker 1.395 km
Athens-Asker 3.470 km
Barcelona-Asker 2.745 km
Frankfurt-Asker 1.445 km
Copenhagen-Asker 635 km
London-Asker 1.945 km
Milano-Asker 2.155 km
Paris-Asker 1.365 km
Stockholm-Asker 565 km
Rome-Asker 2.635 km
Warzawa-Asker 1.515 km

Oslo-Asker 35 km
Bergen-Asker 4972 km
Lillehammer-Asker 215 km
Stavanger-Asker 430 km
Nordkapp-Asker 2.126 km
Molde-Asker 497 km
Swedish border-Asker 110 km
Tromsø-Asker 1.655 km
Vardø-Asker 2.597 km
Trondheim-Asker 518 km
Russian border.Asker 2.450 km

You can charter a seaplane and other types of planes, too, to get to or from the Asker area fast. The seaplane harobur is located in the neigbouring municipality of Bærum, at the old Oslo airport Fornebu - Rolvstangen sea plane harbour.
You got to have some pocket money to be able to do this, though...