抗拒：1. 抵抗, resist; 2. 拒绝, refuse;
抵御：1. 抵挡, 抵抗, resist; 2. 抵御, 预防, protect from;
So, there is an overlap in meaning (sense 1) between these two words. For example, 无法抗拒==无法抵御; 抗拒诱惑==抵御诱惑;
Also, there is a different usage(sense 2) between the two. For example, 抗拒搜查 means you fight against police in order to resist their searching in your home;well, 抵御搜查 would mean that you hide your evidence to protect it to be found out by police; another example is 抵御疾病 means you could wear more to protect you from the disease like a cold; well, there is no direct way that you can fight with diseases, so 抗拒疾病 seems not to make any sense. You can't literally refuse the diseases when they come.