From what you've said, they seem pretty shaky. Employment contracts are becoming more common, though they're certainly not the norm. When most people talk about employment contracts, they're referring to a compensation guarantee. In other words, if your contract is for two years, the company is liable for your compensation if it lets you go after, say, six months. The common alternative to an employment contract is a severance package that's negotiated in advance.
Startups are especially less likely to offer contracts.
There are just too many unknowns that might affect the company's ability to honor a contract. Even at the CEO level, when there's an employment contract it's usually subject to cancellation or amendment in the event of a potential acquisition. The smart thing in this case would be to yoke your request for a contract to their request for any invention rights they want. Change of control usually refers to a buy-out or merger. When negotiating a new job, you'd be better off negotiating for more stock or cash at the six-month milestone, based on your performance, than trying to negotiate an employment contract when the company isn't likely to give you one because it's going to be difficult to honor.