How to run wire through corner with lots of studs
Drill it.  

Just get a spade bit, you have lots of room in the garage opening if that is a stud in the way just start by drilling through that.  Buy some extensions and self feed spade bits.  Drill from the garage opening to the corner then drill from the other direction.  Now to get from one side to the other get 2 fish tapes and insert them and then spin so they hook together then use a plumbers chain with one conductor of your 14/2 looped and twisted through one of the links then duct tape or ele tape the connections and pull your wire.