On 7 June 2006, St Hilda's Governing Body elected to open its doors to men and women alike, starting in Autumn 2008.
The upshot of this is that the first couple of years of men accepted will coexist with an about equal number of women their age and many, many women no more than a few years older than them. I can't speak to the significance of this fact.
According to their website, the nickname for a St Hilda's girl (/boy) is a Hildebeest - pronounced Hill-der-bee-ist, as in wildebeest - although few, to my knowledge, spend any great amount of time frolicking upon the veldt.
Finally, www.balliol.ox.ac.uk is in fact the website for, erm, Balliol College and St Hilda's may be found instead at www.st-hildas.ox.ac.uk.