Are you allowed to lift the football onto your neck using your foot or any part other than your hand, and hold it with your neck, and then walk all the way to the goal and score?
There's no specific rule against it, but I suspect it would be covered by Laws 12.2 and/or 12.3 of the Laws of the Game. These can be found on pages 54-56 of the linked PDF.
Law 12.2 states that players can be penalized with an indirect free kick for "playing in a dangerous manner", which is defined as:
any action that, while trying to play the ball, threatens injury to someone (including the player themself) and includes preventing a nearby opponent from playing the ball for fear of injury.
A neck stall could be considered "preventing a nearby opponent from playing the ball for fear of injury", as anyone trying to get the ball off you would risk injuring you in the process.
Law 12.3, meanwhile, states that "unsporting behaviour" is a cautionable offence. As you stated, neck stalling is not very sporting, so I suspect that any player trying it would end up getting cautioned.