My car shakes at all speeds and it has a nasty burt smell. Lug nuts get lose

You most likely have engine oil leaking on exhaust manifolds or catalytic converters, oil gets burnt there thus you feel burnt smell. Also, you may have coolant leak as well, where coolant is leaking the same way as oil and gets burned around hot engine parts. You should bring your car to specialty shop that will diagnose shaking and burning.