Placing TVS or MOV or Transzorbs for a very basic protection
At these low voltages, a TVS diode rather than a MOV is the standard choice. Typically, each diode is connected from a signal or power line to ground, ideally chassis ground. You indicated that the cable is shielded, but didn't show any connection between the shield and ground. The shield, any metal enclosures, and the ground connection of the TVS diodes should all connect to chassis ground, which should connect to your main power ground at one point.

For ratings, you want the working (reverse) voltage to be higher than the highest voltage you'll normally see, and the clamping (peak) voltage to be lower than the maximum voltage you can tolerate. If you're already running close to tolerances, this can be difficult or impossible: you may need some scaling on the ADC so that it can tolerate more than ±10 V, if your signal can really reach ±9 V.

Another note is that by default, TVS diodes are unidirectional, so if the voltage can go both above and below ground, make sure to get a bidirectional one.

Based on your new schematic, it looks like you're close. You shouldn't need bidirectional TVS diodes on the power supply, since each rail stays on one side of ground (nothing wrong with them, they just tend to cost a little more). Where you do need a (bidirectional) TVS is on the signal line, ideally on both the sensor and receiver. If this is a high-speed signal, make sure to use a sufficiently low-capacitance diode.