The question I guess is pretty clear. I am a physics undergrad wishing to pursue research in quantum gravity(string theory?). What are the subjects I should learn other than the usual compulsory undergrad courses such as quantum mechanics, and GR, etc? Things that come to my mind are QFT, lie algebras, differential geometry, algebraic geometry etc? Other than this, could you suggest any topic that are not entirely essential but interesting in mathematical physics, gauge theory etc (e.g. solitons, monopoles etc). Actually I am looking for a mini project of sorts which would give me an idea of what these fields really are. I have done some lie algebras, classical field theory and am currently studying QM.
First, be proficient in QFT and GR. And by this, not just 'undergrad' versions, but with mathematical rigor -- that includes being fluent in differential geometry and gauge theory. Depending on what type of string theory work you do, and a response to your request of "not entirely essential but interesting", would be to know Algebraic Topology (in order to make sense of TQFT). At this point, you're becoming more of a mathematician -- this is no surprise, it is in essence a mathematical topic. Take a look at Nakahara's textbook "Geometry, Topology, and Physics" for a start (before you begin to think about String Theory).
Physics departments have their research professors decide on candidates primarily on their field of interest, i.e. experimental vs theory, and fields such as solid-state, optics, nuclear, gravitational, string theory, etc. Professors need to fill their labs, and groups like string theory get filled the fastest. A candidate interested in condensed matter physics (experimental) is more like to get accepted into the program, compared to a string theory candidate. If you have already accepted the PhD offer, they will most like try to recruit to into a different group other than string theory. I did experimental physics research for a number of years, and that was the predominant factor that got me accepted into a graduate program.
My post above was probably down-voted because it is skeptical, doesn't directly address the original question; but it is important advice for a candidate in my humble opinion.
From a practical perspective, when it comes to competing with other students for a spot in the string theory group, there are heavy parameters being weighed other than "what you know". You must have research experience, at least 3 years of it; to get into graduate school (for any field), period. Also understand that counselors hear "I want to go into string theory" from 3 out 4 entering graduate students in their physics department. Also, understand that a job in industry is hard enough to find with an experimental physics background, much less resume featuring a cryptic frontier theory. Depending on you conviction for string theory, I encourage you to have a fallback field of study, because chances are you will be put there by the counselor due to the limited space of the theory group.