I don't know how things are over in Denmark, but the "Open Mike" nights around here usually mean that people show up and perform, one after the other. "Open Jams" are a very different thing... the few I've seen quite honestly are just blues nights. There is usually a host band, and you can go up and join in... supposedly. In reality the band just ends up playing the night. But that's just my very limited experience with "jam nights".

Open mike nights, again, there may be a host band. But this is quite different. Individuals or complete bands will have a turn and go up and perform a rehearsed piece. Its not unusual for the host band to back up an individual... an acoustic guitar player may ask them if they know a song, and if they do, they may all play together, or maybe just the drummer and bass player. Most of the time though, the people perform rehearsed songs without backup if they are solo performers, or just their own band members if they are band.

I'd be cautious about how entertaining you'll be trying to "jam" something with complete strangers in front of a live audience... think how rough 1st time rehearsals can be. Better to come prepared to perform a rehearsed piece. If nothing else, you could call or go down to the pub and ask what the format of the evening is meant to be.