It acts like the 'crab-walk' of a 4WD truck when turning? No noises or problems when going straight? No ABS or Traction control engagement? The tires aren't rubbing inside the wheel house on sharp turns?
It sounds like an outer axle joint or differential issue. The LF and RF wheels turn at different speeds on a turn. The differential allows one wheel to speed up and the other to slow down while still applying torque to move the car.
The outer axle CV joints allow the wheels to articulate left or right while still transmitting torque.
If you were to safely jack up the front end off the firm, level ground with the Parking brake set and the rear wheels chocked, the front wheels should rotate by hand (with some brake drag).
In Park, one front wheel will turn in the opposite direction than the one you are rotating. In Neutral (you may have to keep the drivers door closed), the wheels should rotate independently with about equal amounts of drag.
In a past thread, you mentioned that the belly pan was damaged. Inspect the transaxle housing and axles (especially outer plastic boots and joints) for impact damage. Are the joints spewing grease? Any oil leaks? Anything bent or separating? It sounds like the car was bottomed out on something. Check for more damage.
Use jack-stands if crawling under the car. Consult the owners manual or the internet on safe places to jack or support the car frame.