I think it depends on the meaning you use.
In your case of "That is awesome." it means "That is very good.". It is popular in the US. I met two young american girls who are about 20 years old just several times, but the word "awesome" made me impressive, because they often used it. So, I guess it is especially popular among the young people.
Following explanation is copied form the Oxford Advanced Learner's Dictionary.
awesome
1. very impressive or very difficult and perhaps rather frightening
an awesome sight
awesome beauty/power
They had an awesome task ahead
(From the example the dictionary gives, I find that there's always a word after "awesome").
2 (especially NAmE, informal) very good, enjoyable, etc
I just bought this awesome new CD.
Wow! That's totally awesome!
So, that's all that I can help you as a non-native speaker.
Does it make any sense to you?