Take the bus out to Frognerseteren where you'll find marked trails leading to Tryvannstua refuge, Ullevalseter refuge, and then on to Sognsvann (about 18km in all). Dark pine forests alternate with trembling delicate silver birch; there are secret ponds in the forest, lakes, marshes full of lurid green moss, where your boots squelch as you tread; tracks that scramble over pine roots and rock, and lakeside trails. The major trails are well marked, though you take minor paths at your peril - I walked an extra 3 or 4 kilometres in a circle at one point! From Sognsvann, you can take the railway back to the centre of town in just 15 minutes.
Frogneseteren station, reached by bus (train line under repair) from Majorstuen.
Google map: tinyurl.com/33chyvb
The term 'refuge' may better than 'lodge'. There are many around Oslo, all closed on Mondays, and most in July - just when you need them. Right now the Norwegian service is slovenly, the fare uninviting, despite often a queue of hikers. On 15 Sept I paid 30 crowns for a soggy 'vaffel' pikelet, and 30 crowns for a foul coffee, at Skullerudstua in East Oslo ... my Gawd!
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