Could be oil or other fluid getting on something hot and burning. Would be useful to know what kind of burning smell? Does it smell like hot plastic? Burning oil? Cork? Can you be more specific?
If the wheel is shaking, you could have a brake caliper that's partially locked up. This will leave the brakes partially applied on one wheel, which will heat up the rotor to astronomical temperatures (I've had one glowing orange hot), wear out the brake pads fast, possibly damage the rotor and other parts like wheel bearings, and can even cause a fire. And it can make the steering shake.