Turn the cart upside down so that the wheels are easily accessible. Inspect each wheel for misalignment, bent wheel frames or wheel looseness. If the screws securing a wheel to the cart are loose, tighten them with a screwdriver.
Wipe away any dirt and grime that may contribute to the wheel's wobbliness. Coat the wheel with bleach cleaning spray and wipe it down with a thick rag. Thoroughly clean all parts of the wheel, including inside the wheel harness. Allow the wheel to air dry for about 10 minutes.
If the wheel still squeaks and wobbles, spray penetrating oil on the wheel, its axle and its bearing. Allow the oil to penetrate the wheel's assembly for five minutes before using the cart.
Replace a wheel that is rusted or broken beyond repair. Replacement parts can be ordered online and from specialty retailers. Order a replacement wheel that suits the cart's specifications. Remember to order compatible screws that will match the cart wheels.
Remove the screws that bolt the wheel inside its harness with a screwdriver. Insert the new wheel inside the harness and replace the screws.
Lubricate the replacement wheel with a penetrating oil spray every few months. Lightly coat the new wheel so that it rolls smoothly and to prevent rust and dirt accumulation.