There is a lot of overlap and probably there is no rule that will ensure 100% accuracy of use. You need lots of examples. However ........ The phrase 'on the spur of the moment' may be used when you make an instant decision or instinctively do something in reaction to something that happens unexpectedly. E.g. a car was coming towards me and on the spur of the moment I dived into a ditch by the side of the road. 'On a whim' signifies that without analysing the situation, an opportunity presents itself for you to do something .... and you just do it. Why not? E.g. I saw this nice shirt in the shop window and even though I am penniless, on a whim I went in and bought it. 'On impulse' can be used more or less in the same way as 'on a whim' but can also signify that you have reacted instantly to something when you could have just ignored it. E.g. this bloke gave me a really evil look and on impulse I punched his lights out!