Raiden slashes his sword when he dodges, so it's a good way of avoiding an attack while keeping up the pressure on an enemy. You've probably noticed with Blade Wolf that if you just parry an attack he'll bounce off you and land out of attacking range, giving him a chance to attack again. If you dodge his attacks instead you can keep chipping away at him the whole time.
There's a neat video of a guy destroying him without ever parrying, just always dodging so he manages to keep Blade Wolf in sword range.
Generally, a perfect parry (which is when Raiden automatically counter attacks after a block) is the best way of taking out an enemy quickly, but the timing's really tight on higher difficulties and I've never been able to pull them off at will. Plus I don't think every attack in the game can be perfect parried, and even if they can a lot of enemies will jump around so much that your counter attack won't hit them. The elite soldiers you'll meet up with soon will actually counter attack your counter attacks, too. It's a good idea to get used to a combination of parrying and dodging, just try it out on various enemies and see what works best for you.
Some enemies will have un-parry-able attacks, too, and those you'll need to either dodge or Ninja Run away from. They're telegraphed by a yellow flash from the enemy (whereas parry-able attacks will flash red), and it's usually a grab move of some kind that you'll need to clack the stick side to side to break out of.