If you have +/- wires for each signal, then you have an industrial-style encoder with differential signals, designed for noise immunity over long distances.
ODrive takes single-ended signals. You can convert the signals with an RS-422 receiver chip like this one:
These are the Hall sensors. They are like a very low-resolution encoder, used by more simplistic drives. They have six states which repeat for each pole-pair, so their resolution is only 6 * N_pole_pairs counts per turn.
It is possible to run a brushless motor a bit like a brushed motor, using nothing more than Hall sensors and MOSFETs. The Hall sensor detects which phases need to be energised to form a basic six-step commutation sequence.
However, with six-step commutation, there is no torque control, so it is less efficient, less precise and less controllable than it can be with Field-Oriented Control (FOC).
FOC is a more advanced control scheme, using the precise position of the rotor and a PWM inverter to align the field so that it always produces a torque proportional to current, and it requires a high-resolution encoder.
The short answer is that Hall sensors (UVW) can be used for coarse control of a motor (e.g. for E-bikes etc) whereas FOC is more precise and can be used for motion control and precise positioning in robotics applications, but it requires a high-resolution encoder.
If you have both ABZ (incremental encoder) and UVW (Hall sensor), on both motor and drive, then ABZ is usually superior.
Some drives can accept both simultaneously. ODrive doesn’t officially support that.
The UWV hall sensors in servo motors are used to track the stages of communication so you don’t have to calibrate the motor from the start. Moving the motor to calibrate isn’t really feasible for most servo applications so a simple hall commutation encoder takes care of that. Then the actual FOC calculation is done with the incremental encoder.
Note that you need to disable the brake first to move the motor. Which needs 24V so you need a relay for this.