Scala, 120 bytes
readLine.inits.flatMap(_.tails).toList.groupBy(l=>l).filter(x=>x._2.length<2).map(_._1).groupBy(_.length).minBy(_._1)._2
I started off with 140 which at least already fits into a tweet.
( // added for comments
readLine // input
.inits.flatMap(_.tails).toList // get all substrings of that string
.groupBy(l=>l).filter(x=>x._2.length<2) // remove substrings that occur more than once
.map(_._1).groupBy(_.length) // take the substring and group by length
.minBy(_._1)._2 // take the list of shortest substrings
)