I am from India, but currently a Doctoral Candidate with an Italian University. I have been selected by Oxford University, UK for the Academic Visitor Programme for a period of one month. I have to conduct my own research, I am not a part of any research project of Oxford (so cannot be business visitor) and I am to use the facilities to work on my own.

After going through various visa types I contacted the Oxford University indicating that I may need a "Short Term Student Visitor" Visa and for that I need a letter to which the University replied that I need to apply for "Academic Visitor" only as I would not be "enrolled" as a student and I should ask for a letter from my University in Italy saying that they are giving me leave for the duration of visiting programme and that I am coming for exchange of information and experience and conduct my research. Further, since my Italian University will completely fund the Visiting Period, it should not be a problem.

I read here http://www.postgraduateforum.com/thread-12278 that it is possible for a PhD candidate to get an academic visitor visa if I have a academic repute, strong CV , leave and funding. Is this acceptable as I am a bit confused as in the entry where the Visa application asks "student" or "working" what should be my answer if I am working on some projects along side my PhD?

I would be really thankful if someone would help me with suggestions on making the application stronger.

You need to contact the Home Office and ask them I think, to ensure you get the correct answer. You are right though, you won't need a student visa, because you are coming as an academic visitor.