Ummm, don't know if there's a running club, I haven't noticed one.
I've never set up a society but one of my friends has and I think you need at least 20 ppl, to organise for there to be a committee and have an annual AGM. If you go to the union I believe you register your society there and they sometimes give some funding. Oh yeah, and I think there has to be a membership fee...but it can be minimal, like £1 a year.
I would recommend dancesoc....lots of diff classes for £5 a year (and you have to have sports centre membership which is about £27). For example last year I did Latin Jazz, HipHop and Theatre dance and you get to be in the show at the end of the year which is a really good experience.
Also, celticsoc is great....most friendly society I've come across. The lessons are fun and you can show off your skills when there are ceilidhs. :-) If you get more involved there are proper scottish country dancing balls...they have the Highland Ball in St Andrews and other ones in Edinburgh, Aberdeen and so on. There are weekly socials after the intermediate class too which beginners are welcome to go to as well.
I joined the riding society but I didn't find them very welcoming and they were rather disorganised. But it can be good if you want to ride and have no transport. Though the edenside stables can be reached by bus/bike ride.
Other than that I just joined academic societies....they're useful to be in to get to know people doing the same subject in different years.
So, yes, I've rambled on a bit....I just finished work and have time on my hands, lol. Societies can be a major part of your social life. :-)