var strings:Array = ["one","two","three","four","five","six"];

// create a clone of your array that represents available strings  
var available:Array = strings.slice();

// choose/splice a random element from available until there are none remaining
while (available.length > 0)
{
   var choiceIndex:int = Math.random() * available.length;
   var choice:String = available[choiceIndex];
   available.splice(choiceIndex,1);
   trace (choice);
   // you could create a textfield here and assign choice to it
   // then add it to the display list
}

var source:Array = ["one","two","three","four","five","six","seven","eight"];
var displayedIndices:Array = [];

var index:uint = Math.floor(Math.random())*source.length;
displayedIndices.push(index);
var newString:String = source[index];
addChildAt(myTextField(newString), index); //I suppose myTextField creates a textfield and returns it

//now you want to be sure not to add the same string again
//so you take a random index until it hasn't already been used
while (displayedIndices.indexOf(index) != -1)
{
   index = Math.floor(Math.random())*source.length;
}
//there your index has not already been treated
displayedIndices.push(index);
var newString:String = source[index];
addChildAt(myTextField(newString), index);