transverse.js

var transverser = function(obj) {

  var result = [];

  var pusher = function(str, arr) {
    arr.forEach(function(obj) {
      if (obj.perms) return pusher(str + obj.value, obj.perms);
      result.push(str + obj.value);
    });
  };

  pusher('', obj)
  return result;

};

var res = transverser([{"value":1,"perms":[{"value":1},{"value":2},{"value":4}]},{"value":2,"perms":[{"value":1},{"value":2},{"value":4}]},{"value":4,"perms":[{"value":1},{"value":2},{"value":4}]}]);
console.log(res);