Hi younggreek. As you said βίωσε βίο(ν)! is the exact translation of live life! But in greek it doesn't sound that good. Not that it is wrong but I don't know if any Greek would ever use the structure you are suggesting of .
If I was to say live life! I would say something like ζήσε τη ζωή! (live the life). Or something more emphatic like βίωσε τη ζωή.
To make myself clear to you, βίος has the meaning of works and days of somebody, at least in modern Greek. A short of biography.
So as regards to the noun, ζωή must be the word you are looking for. Ζωή means the state of being.
Now the verb ζήσε which actually means live is ok. But if you want to be more emphatic use the verb βίωσε which includes the situation of feelings and emotions.
If you want my opinion, I really liked the Ancient Greek suggestion of dear billbergs23 of ζῆθι.
Il give you all three, in three different fonds (I like the first one)http://www.4shared.com/file/140045241/9565cda7/_online.html
We can also wait to see what other comments may be writen.