And I am still playing the good old Thief II. Now since I am on the last Level I am only derping around trying to figure out the best ways to kill those Blue Robots (and these newer Sawblade shooting Spider Robots)
Here a few Strategies I came up with over the time:
1. Shoot up to two Water Arrows into the red glowing Boiler Vent opening on the Back Side to shut them down, this is ofcourse the standard way of disabling them.
2. Shoot Fire Arrows (those are explosive) until the Robots shut down or break. Expensive but it works. I would save my Fire Arrows for the Cameras however.
3. Place a Mine and wait until they walk over it. This kills every kind of Robot as long as the Mine is placed properly, so that they walk straight into it and not just run past it triggering the Mine from too far away to be killed with one hit.
4. Use the Blackjack (basically a small Metal Bat, normally used to knock people unconscious) and hammer with it on the Robot until it errors out. This even works on the large Blue ones (yes, the ones with the Bomb Gun) if done properly. That actually works! You might die from the Bomb Fire, unless you constantly run around it counter-clockwise, but it works. You have good chances if you are at full health, since it can occassionally still hit you once. But you need a way to get close to the Robot without it seeing you, before you start hammering, so sneak from behind.
5. Use the Bomb Fire of other Robots or Turrets to destroy each other. This might sound hard but it is pretty easy, since they shoot even if there are other ones inbetween.
6. Let the Robot shoot itself. Just hide in a small gap in a wall so that they come so close to you that their Right Arm shoots against the Wall instead of hitting you (since it shoots Bombs, they explode after a few secs). This Method can be enhanced by using the Blackjack on the Robot while it kills itself. This Method doesn't work if you have two Robots chasing you.
Edit: I found another nice Method, and the best is that it is free!
Use Noisemaker Arrow to lure Robot into darkness, and then attack it from behind. That way the Robot cannot see you while you smash the hell out of it. Just shoot the Arrow at a Location where you can retrieve it back again.