Hi,
They can't do shit. You can just walk away from any job with no notice at all. The only thing they can do is not give you a good reference in future. I wouldn't give a flying fuck about reference. Now this is regarding quitting. But if there is a conflict of interest working for this new company, it's a different story. For example, the new company is a customer of current employer and you are contractually bound to not work for any of their customer due to trade secrets or other similar reasons. Also look at your states law on quitting. State law can override any mickey mouse contract. Like someone suggested earlier I would keep record of all communication and conversation. Telephone, verbal conversation doesnt mean squat. Its all here and say. Hard evidence of written communication is what matters. Honestly, I would scare the shit out of them by telling them that you will be seeking legal action against them for all sorts reasons like threat, extortion, lunch hours, breaching labor code, unpaid overtime, making u pay for application and tens of other things you can come up with. In Trumps USA, that would scare the bejesus out of them.
Ciao,