gistfile1.js

var words = "orman roman tilki kilit iri kirli kuzu at rahat karat tarak".replace(/[^\w\s]+/g,'').split(" "),
    dict  = createDict(words);

console.log( 1, anagrams("tikil") ); // tilki, kilit
console.log( 2, anagrams("atkr") ); // karat, tarak
console.log( 3, anagrams("armon") ); // roman, orman

function createDict(list){

  var i = words.length,
      el, result = {};

  while( i -- ){
    el = sort(words[i]);

    ! result[el] && ( result[el] = [] );

    result[el].push( words[i] );
  }

  return result;
}

function sort(word){
  return word.split('')
    .filter(function(el, ind, list){
      return list.indexOf(el, ind+1) == -1;
    })
    .sort(function(a, b){ return a > b; }).join('');
}

function anagrams( word ){

  var letters = sort(word).split(""),
      result = "";

  while( letters.length > 2 ){

    result = letters.join("");

    if( dict[ result ] ){
      return dict[result];
    }

    letters.pop();

  }

  return undefined;
};