Calamity is a very old-fashioned word - it has the same meaning as the other two to me, but it is so rarely heard that I don't feel it's really worth adding to your vocabulary. If you're just talking about a general bad event, then I'd say both disaster and catastrophe would work. For example: I just finished the test. I did so badly, it was a disaster! I just finished the test. I did so badly, it was a catastrophe! The only case in which there is a distinction is when you're talking about natural events. For example a tornado, an earthquake, a flood etc. Then you would use the term "natural disaster", e.g. "It is believed that global warming will contribute to a higher frequency of natural disasters in the coming years". You can't use catastrophe in this sentence.

Thank you, one more questions, can I use"catastrophe" or "disaster"to describe a bad situations that the human did. eg:invade , which is prefer to chose? thank you~