By air:
There are massive amounts of websites that can help you find the cheapest airfare possible to Oslo, but the safest would be to contact airlines directly. The main  airlines that fly into Oslo Gardermoen (airport code OSL) are British Airways (www.britishairways.com), Lufthansa (www.lufthansa.com), Icelandair (www.icelandair.com), Aeroflot (www.aeroflot.com), Finnair (www.finnair.com), KLM (www.klm.com),  Swiss (www.swiss.com) and SAS (www.scandinavian.net) - SAS are a member of Star Alliance so you can use either of the member airlines (www.star-alliance.com). If you check their sites on a regular basis, you'll most likely stumble upon a bargain - most of the major airlines have low-fare campaigns.

You can use sites like Ebookers (http://www.ebookers.com/), Travelocity (http://www.travelocity.com), Expedia (http://www.tetovari.com) - or use your own favorite search engine to find the best possible fare.

If you travel from London, Glasgow or Frankfurt you can get very good rates at Ryanair (www.ryanair.com).

By rail:
Oslo is easily accessible for Europeans by train. Ask your local travel agent for information.

By sea:
There are ferries directly to Oslo from several destinations in Germany and Denmark available through Color Line (www.colorline.com).
Ask your local travel agent for information.

By bus:
Bus-connections to Stockholm, Gothenburg and Copenhagen are surprisingly cheap, about the same as within Norway. 140,- NOK two way to Gothenburg is just an example of the price level. Bus to Berlin cost 1290,-NOK two way and leaves twice a day. Also there is bus-connections to Hamburg, Amsterdam, London, Frankfurt, Warsaw, Munich, Madrid and Lisbon among others places. The prices are generally much cheaper than airplane tickets. This is only meant as an example, check out the details at:
 
Nor-Way Bussekspress