Why not look at the words themselves? Cool: low temperature... calm, easy, effortless Awesome: some awe! ...awe-inspring, fascinating Smashing: something exciting... like a car smash. Or smashing plates. Groovy: in a groove. Like the grooves on a vinyl record. Also a groove has a direction, so you'd guess whatever's in the groove (and therefore groovy) is going somewhere. It's fun to work out the analogy. :D

The difference comes in the context that you use the word...like if you see a football player score a great goal, you could say "cool!!" or "that was awesome!" There wouldn't be much difference as you will be implying that you are impressed with the goal. But it would sound a little weird if you say "that was a groovy goal" It all depends on the situation. The more you speak English and watch movies, the more you will become comfortable with using the right word in the right situation... :D

they are all common descriptive words. smashing and groovy are probably less current than cool and awesome.

They are all informal words that describe somebody or something that is 'very good' or 'excellent'. 'Bad' is the antonym. 'You look smashing!' 'His song's really cool.' Awesome (=inspiring awe or admiration or wonder) 'It's totally awesome!' 'Check out the new cafeteria! Awesome!' 'Groovy friendship' ("groovy" is essentially dead, "cool" is a word that has proved to be popular over a long period of time. In fact, it is general colloquial language, especially in America.)