I assume that compared to a tripod, image stabilization reduces image quality in the same way that higher ISO speed reduces image quality in comparison to low ISO speed.
Image stabilisation is not a dial that you turn up or down to trade stabilisation against image quality. Ignoring panning modes etc. it's either on or off.
The appearance of camera shake is somewhat random, at a given shutter speed there is a certain percentage chance the image will contain small enough blur to be unnoticeable. When image stabilisation is turned on you'll get roughly the same percentage chance but at a shutter speed many times slower. So if you're getting 75% sharp images at 1/50s then with IS you might get 75% sharp images at 1/5s.
The important thing to note is that [ignoring subject motion] the sharp images at 1/50s without IS will be of the same quality as the sharp images at 1/5s with IS.
There is therefore no equivalence between IS and increasing sensitivity using ISO to allow faster shutter speeds, as the use of IS has no theoretical impact on image quality, unlike increasing sensitivity with a shorter exposure which will lead to increased noise. It's actually a price/image quality tradeoff, i.e. the question you need to ask is how much increase in ISO speed is worth the cost of an IS lens.
If you're ignoring noise and asking what change in ISO results in the same reduction in camera shake as the use of an IS lens, then the question depends on the particular lens. Manufacturers state the performance of an IS system in terms of how many stops you can decrease shutter speed for a comparible level of camera shake. The figures tend to represent the best case, in reality the performance could be a stop worse in the worst case. So...
2-stop IS is approximately equivalent to going from ISO100 to ISO200 in the worst case, ISO400 in the best case
3-stop IS is approximately equivalent to going from ISO100 to ISO400 in the worst case, ISO800 in the best case
1 stop is a doubling of the ISO number, 2 stops is quadrupling, N stops is increasing by a factor of 2 to the power N.
Unfortunately it's a hard question to answer as it not only varies from camera to camera, but it also depends on your starting point. Moving from ISO100 to ISO400 (with suitable increase in shutter speed) will have a small impact on image quality compared with moving from ISO1600 to ISO6400.
Good handholding technique is not that hard, even if you consider yourself to not have steady hands. Stand with feet apart than then set up a "tripod" using your arms and bracing the camera against your face via the eyepiece to make the third leg (this can be uncomfortable if you do it really hard, but you only need hold the stance for a few seconds). Set the camera to continuous shooting and then fire of at least 5 frames to maximise your chances of getting a sharp image.
