Do you have an actual written job offer, with a specific start date? Because from my perspective if I don't have that, then I don't have the job. Asking you to coordinate your own orientation is just weird to me.

I've had a couple of potential jobs, be weird with me, and jerk me around like it sounds they are doing with you. In one case it was a question of the interviewer not having the actual authority to hire anyone and in the other the interview was uncomfortable with my request for flexible work hours but just didn't want to tell me that.

I get how stressful it is when we're desperate for work, but honestly if you don't have an offer letter, I'd simply get in touch with whoever offered you the job verbally, and say you're waiting for an offer letter spelling out salary and start date. If you get it great, if you don't get it, then you know they're not professional and you've probably dodged a bullet.