By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation $$sum_{i,j=1}^{N}D_i(a_{ij}(x){parallel}Dy{parallel}^{p-2}D_jy)+{langle}b(x),;{parallel}Dy{parallel}^{p-2}Dy{ angle}+c(x)f(y)=0,;p>1$$. The obtained theorems include and improve some existing ones for the undamped halflinear partial differential equation and the semilinear elliptic equation.