I theory, you could track angular orientation and XY displacement using 3 unpowered
omni wheels with one encoder on each.
See attached sketch.
3 unpowered omni wheels L, R, & C, with one encoder on each wheel.
Forward (FWD) is upward in the diagram, strafe right (STR) is to the right in the diagram, rotation (omega) is positive clockwise.
The red dot is the reference point of robot motion (typically, but not necessarily, the center of the robot).
Here's how to convert the L, R, and C encoder speeds in fps into robot-centric motion FWD, STR, and omega:
FWD = (L+R)/2 fps
STR = C fps
omega = (L-R)/W rad/sec