ORDER BY key->>1::int, key->>2::int, key->>3::int
There is no easy way, presently, to convert from a json array to a PostgreSQL array. If you do that I believe that those sort based upon the values and not lexically.
SELECT *
FROM ( VALUES (ARRAY[2014]::int[], ARRAY[2014,2]::int[], ARRAY[2015]::int[]) ) vals (v)