Extremely drunk, especially to the point of becoming incapable of making rational decisions. A reference to the character Otis Campbell, the town drunk on The Andy Griffith Show. We all sat in the back of Matt's pickup truck, slamming beers and tequila until we were all Otis drunk.
Otis
(ˈotɪs)
1. n. a drunkard. (From the name of a television character who is the town drunk. Also a term of address.) Look at Otis over there, propped up against the wall.
2. mod. drunk. Fred was Otis by midnight and began looking like he was going to barf.