Erm... Oxford and Cambridge look at Extracurriculars where they directly relate to your interest in and aptitude for the subject you have applied for ie: medical work experience for medicine applicants or giving a talk to a history society for a history applicant (who can then talk about the research they did and how it developed their skills/understanding). Building houses for the homeless in Africa is irrelevant for a Maths applicant (for example) and will not sway the interviewers. Oxford tells you to include a small amount of this stuff if you have done it because they know you are applying to other universities who might care.(Original post by ThatOldGuy)
Go ahead and apply. There's always a chance.
For instance: How much volunteer work did you do in Africa building houses for the homeless? How much work do you do with the Big Brothers association over here?
Oxford and Cambridge both look at Extracurriculars an awful lot, so if you didn't just sit at home and moan about not getting in to Oxford and have been working really hard to build up your CV for Oxford, you probably have a decent chance for a non-STEM subject.
On the other hand, if you just really want to get in to Oxford and didn't do well, your chances are practically non-existent.
Oxford's advice on personal statements and extra curriculars is here.
Would you pay less for a humanities degree?