For a 27-year-old, Harvard Extension might be more appropriate than Harvard University (same campus, same professors, but with a non-traditional/older student focus). I would check that out as well.
Can you get admitted? Well, it is easier to get admitted to Harvard Extension than to Harvard University. A 3.38 GPA is low, although I am not sure what accomodations would be made for your circumstances. Top schools have admitted refugees from overseas camps before (usually with very high grades, though). You would have to take an SAT and TOEFL at some point. I don’t know how you’d go about arranging that, but it sounds like your online school might be of help.
Good luck!