According to Wikipedia, the concept of horror-comedy dates back to Washington Irving's "The Legend of Sleepy Hollow," first published in 1820. It's a well worn genre at the movies, but this one is new: cutesy-horror.
"Odd Thomas" is based on a story by Dean Koontz that I haven't read so I'm unable to comment on the quality of the conversion process. Odd is, as his name suggests, a little unusual: he sees dead people. And yes, there is a bit of "The Sixth Sense" about it, with Odd using his ability to see a young girl who was recently raped and killed to find and catch the killer. It's also established that the town's police chief (Willem Dafoe, kind of wasted) knows about Odd's skills and helps him out. All fine so far. But then we're introduced to Stormy (Addison Timlin), Odd's girlfriend - and their hyper-cute relationship that is repeatedly referred to as being meant to last forever. And now we're given the motivator for the main story arc: a man comes into the diner where Odd works, surrounded by "bodachs," evil spirits that only Odd can see that presage multiple deaths. The majority of the film is Odd trying to figure out what's going to happen and then prevent it.
The primary problem is the tone of the movie. For me, Odd's upbeat personality and attitude didn't make any damn sense for someone who spends a fair bit of his life following ghosts and helping apprehend murderers. And his relationship with his girlfriend is nauseatingly cute, which has no place at all in a movie that's trying to have anything to do with horror. Yelchin tries hard, and Dafoe helps when he can but is seriously underused. Just a lousy movie.