LetX be a smooth algebraic surface over the complex number field. Fix a polarizationL, an invertible sheafc1 and an integerc2 such that (4c2-c12) is positive. letML(c1,c2) be the moduli space ofL-stable locally free rank-2 sheaves onX with chern classesc1 andc2 respectively, and let ξ be a numerical equivalence class defining a nonempty wall of type (c1,c2). We study the properties ofEξ(c1,c2) and obtain estimations for its dimension. Then, we discuss the existence of trivial polarizations, and determine the birational structures of moduli spacesML(c1,c2) whenX is a minimal surface of general type and (4c2-c12) is sufficiently large.