Can one daven Drunk and what is the Level of drunkenness that disallows one from Davening?
Preferably one should not do so, though after the fact his tefillah is valid - unless one is so drunk that "he would be unable to talk before a king," and then his tefillah in such a state is invalid. (Shulchan Aruch, Orach Chaim 99:1)
Rema (ibid. :3) comments that "we're not concerned about slight drunkenness" when it comes to present-day wines (which are weaker, either in alcohol content or in viscosity, than Talmudic-era ones) - the more so if one is davening from a siddur. Nevertheless, Pri Megadim says that it's not a proper thing to do.
You can daven drunk until you slur your words:
If one drank to the point that he is unable to speak in front of a king without slurring his words, then it is forbidden for him to Daven Shemoneh Esrei until he becomes sober.
Footnote 9 describes 2 states that are forbidden to daven-
There are two levels of cannot speak properly before a King regarding this matter. 1) One who cannot talk without a slur, but can talk fluently without stumbling on his words. This is called Shasuiy. 2) One who cannot talk without stumbling on his words. This is called Shikur. [185:5] The state of Shikur is more stringent than the state of Shasuiy