How difficult is it to get into Oxford's graduate program?

Yeah, ECs don’t matter for graduate admissions, especially not for an academic DPhil. The emphasis is going to be on your grades, your letters of recommendation, your writing sample, and your research proposal.

What kind of advice are you looking for? These forums are great but you’re unlikely to find a student of that program, or a faculty member, here able to give you very specific/first-hand advice other than what you find on the website.