Start it and run it in the garage / driveway,etc, without moving it. If the smell comes up , then it is NOT brakes related.
If you have to drive it around for the smell to re-appear then it IS brake related.
It's probably not burning oil, unless the engine gaskets are leaking quite profusely. Oil burning smell different and comes out the exhaust.
It is something that is getting on hot (probably exhaust manifold or pipes) engine parts., or as noted the rive belt(s). Most cars will lose AC, power steering, alternator and water pump if the belt(s) go,. You would have a few minutes at best before the car overheats to the point of eventual engine bearing failure.
The reason the smell appears strong when you shut it off is because the engine cooling fans are blowing the odor away while the engine is running.