Okay, so on a basic level three things make up an elite unit, training, equipment and esprit de corps. These factors tend to contribute, in various degrees, to making an elite unit.

Knights are a good example, their equipment, life long training and mentality made them stand out on a medieval battlefield as the absolute elite. Spartan warriors are another example, however their equipment was less specialized and the emphasis was on training and mentality. Riflemen in the Napoleonic wars are an example where equipment made a unit stand out.

I brought up these examples mainly as a frame of reference and background against which to analyze the Waffen SS:

Training - Generally speaking the training of most Waffen SS units was not significantly different or better than the average german soldier. Early in the war, especially during the occupation of Poland and in the early days of some specialized divisions (Nordland for example) it was probably significantly worse.

Equipment: The Waffen SS often had priority on recieving new equipment and supplies but their equipment was not generally speaking vastly superior or different from the norm.

Esprit de corps: This is where the Waffen SS really stand out. They were to a large degree convinced that they were the absolute elite. In some sense it was a self-fulfilling prophecy. They were willing to risk more, endure worse odds and accept greater casualties than conventional units, this allowed them to achieve tactical victories where other units probably would not have.
However, the flip side is that they did this at the cost of far greater casualties than almost any other unit in the war and they were frequently, and probably rightfully, accused of taking unnecessary risks.

Were the Waffen SS an elite unit? Yes, their loyalty and devotion to their cause and in some sense their own reputation made them an elite unit although often at the cost of high casualties.