Inebriated is just a fancy way of saying drunk. If you see a man staggering down the street grasping a bottle of rum in his hand, chances are he's inebriated.
When you want to use an impressive word to say that someone is drunk, go ahead and use inebriated. If you like, you can also use it to refer to someone who is intoxicated with substances other than alcohol, but at its heart, inebriated simply means tanked, blotto, stinko, drunk. In more recent years, it has taken on the sense of being particularly energized or zany and exhilarated with drunkenness, but still drunk.