mellink, the gain you describe given the ratio of resistances specified is correct; specifically Acl(NI) = 1+RF/RI, whereas Acl(I) = RF/RI. If either of these formulae are not obvious, google inverting and non-inverting operational amplifier circuits.
Using a stepper motor as an input device (rather than using a potentiometer or an encoder) is a hack to begin with. There are two flavors of stepper; Unipolar which typically have 5 or 6 wired connections, or Bipolar, which typically has 4. I suggest that you research this topic further to determine which you have at least, or the differences between the two, how they're typically wired, how they're driven etc.
Using a Stepper as an input device, when it is stationary, it behaves (the windings at least) as would a low value resistor network. Perhaps this is why your OpAmp circuit is saturating; the other end of the winding is at +V potential, amped by 11, = saturation.
Stilll when a stepper is forced to move by outside force, voltage spikes of the order of typically hundreds of volts (if there is no significant current draw) are induced, and depending on topology could be of either polarity. Spikes produced will likely exceed above/below ground potential for the devices in question, requiring the use of clamping diodes and other such circuitry to avoid downstream destruction. Driver circuits for these motors (integrated circuits) typically employ diodes to protect themselves from destruction.
So basically they suck as encoders or input devices (no matter how cheap they are surplus) as the additional components necessary to use these (safely without wrecking other devices) beyond their intended purposes not to mention the additional R&D, just don't produce a sound design.
I would suggest instead that if you're using an Arduino product, that you consider using potentiometers for A/D inputs if not encoders for digital input devices. Not even sure why the OpAmp is required in your particular case, but perhaps you can dispense with the OpAmp if not the stepper motor entirely; are you trying to sense relative movement, or sense amplitude?
Not clear on what you want, but I hope that I've suggested adequate avenues of research regardless.
DHM