Six types of moiré superstructures of graphene on Ir(111) with different orientations (labeled as R0, R14, R19, R23, R26 and R30) are investigated by low-energy electron diffraction, scanning tunneling microscopy and first-principles calculations. The moiré superstructure of R0 graphene has remarkable diffraction spots and deeper corrugation than that of the other superstructures. A high-order commensurate (HOC) method is applied to produce a list of all possible graphene moiré superstructures on Ir(111). Several useful structural data including the precise matrices of the moiré patterns are revealed. Density functional theory based first-principles calculations that include van der Waals interactions reveal the differences of the geometric environment and electronic structures of carbon atoms with respect to the underlying Ir(111) lattices for all the observed moiré patterns. The further calculations of electronic properties at the graphene-Ir interfaces show that the electron transfers for all superstructures are small and of the same order of magnitude, which demonstrates a weak interaction between graphene and the Ir(111) substrate, leading to the coexistence of multi-oriented moiré superstructures.