Stepper motor oscillates instead of rotating in the particular range of RPM (100-150). It does rotate when I change the speed (StepRPM) below 100 and way above 150 i.e. up to 900 RPM.
Sounds like you have encountered resonance. Enable microstepping will mitigate resonance effects. X4 to X8 at least. I have motors that shudder/stop that at 200 steps/sec, no microstepping. Setting microstepping to x4 helps a lot.
And/or use some damping in the mechanical drive (belt drive is better damped than lead screw, for example).
Can you please post a circuit diagram of your project.
An image of a hand drawn schematic will be good, please include all power supplies, component names and pin labels.
Can you post links to stepper and driver units spec/data please?