INCAPACITATE: THE GREAT EQUALIZER
I'd argue that the middle clicks of life are the most powerful for Quasar because of Incapacitate and a double-ranged attack (and a very useable range of 8). Having Running Shot allows you to move 5 spaces too, giving Quasar an effective 13 range to smack 2 people with Incap. Why is Incapacitate so great? Because it doesn't matter if your opponent has Impervious or Invulnerability -- Incapacitate will stop them in their tracks (and force them to push if they don't have Willpower). It truly is the Hulk/Superman stopper.

For you Golden Age players, you may be tempted to throw Stunning Blow on Quasar, but don't do it! It's not worth it, and you'll be kicking yourself if Quasar takes damage that throws him past his Incapacitate.

Here's another great idea -- use Running Shot to run away from your opponent (which most players don't do), and will frustrate those close combat Wolverine-type figures. Staying at a distance is important since Quasar only has Energy Shield/Deflection for the rest of his dial. Note that these are also his utility clicks of life, so use that Enhancement if you can -- but I would prefer to keep Quasar there as a primary attacker with Incapacitate.

The last couple clicks of life is pretty weak, but Quasar's defense get's a nice little bump. The most important ability here is Telekinesis, which has a whole slew of possibilities. Rather than running away to a Support ally, I think you should keep Quasar in the fight. If you've got a melee friendly nearby, use Telekinesis to put him/her into position for a powerful attack!