根据题意,全集U={x∈Z||x|<5}={-4,-3,-2,-1,0,1,2,3,4},B={0,2,4},
则∁ UB={-4,-3,-2,-1,1,3},A={-2,1,3,4},
则A∩(∁ UB)={-2,1,3};
故选B.