@fossheim Hey, I don't know if this is within your "no" criteria, but I personally worked with creating some hiking tips for Oslo called Grønne Sykkelruter, which you can find at grønnesykkelruter.no. Maybe you can have a look at see what you think.
Otherwise I think following the newly opened Hovinbekken is really nice. And also the green strip along the T-bane linje 5 from Økern towards Groruddalen, and the green strip in Groruddalen to Hølaløkka