The coherent and the incoherent interactions of discreet solitons in quasi one-dimensional optically induced photonic lattice are theoretically and numerically analyzed. It is found that in-phase solitons attract each other and out-of-phase solitons repel one other. Due to the anisotropy of the nonlinearity, two initially attractive incoherent solitons will repel each other as their interval waveguide number increasing. Moreover, the pendulum-like intertwist of discrete solitons is observed during the incoherent interaction due to the interplay between soliton transverse motions resulting from the soliton interaction and the Bragg reflection of the lattice structure. These results help us to understand how the anisotropy of the nonlinearity response plays a role in discrete soliton interaction and offers the theoretical support for the experimental investigation.