I did not hear 一般过去时。我没有听过。例句: I did not hear about how he died yesterday, do you know? 翻译:我没有听过他昨天怎么死的,你知道吗?(这个例句有点烂,将就吧。。)
I have not heard 现在完成时。比较像是‘我还没有听过’。例句: I have not heard about the latest news yet, have you? 翻译:我还没听说最新的消息,你呢?
I have not been hearing 现在完成进行时。我已经没有听过。一般和‘since’用在一起。例句: I have not been hearing any news about him since he went oversea last year. 翻译:自从他去年出国(或‘去海外’),我就已经没听过他的消息了。