The swashplate should only move up/down in response to collective stick input, not change its tilt in any direction.
Did you go through the servo check per the manual (disconnect both motors, noting the orientation of the plugs)?
With the motors disco. you should see the swashplate moving smoothly down/up in response to moving the collective up/down. It sounds like somehow one or more of the servos are binding or have stripped gears, or possibly the control arms are a little bent and not rotating freely enough in the servo yokes so that causes binding.
Before I fly I always work the cyclic around a couple of times just to catch any gross problems with swashplate response to servo input.