Most cities have free walking tours - you are expected to tip your tour guide, but it's still relatively cheap.
There are some great free museums in London if that's of interest - the Tate, British Museum, British Library, Victoria & Albert.
I haven't been to Oslo, but I've heard food there is outrageously expensive. It might make sense to pack some food/snacks in your bags for that portion of the trip if it is feasible.
Also, one of my coworkers travels extensively and the place he's raved about most is Bruges, so definitely consider going if the timing/budget works out.
ETA: Given your interest in partying/nightlife, you might want to look into beer/wine/liquor tastings and pub crawls. I have fond memories of the Bombay Sapphire distillery in London and the Heineken Brewery in Amsterdam and I'm sure there are far more interesting places that I was too young/naive/unsophisticated to partake in when I did my backpacking across Europe trip many, many moons ago.