What can I do if the terms of my adjunct contract are not what I was led to believe they would be?
First of all, consult a lawyer before doing anything.

If you were to leave in the middle of the course, that will cause havoc, that they won't probably want. Since they are not paying you for the work, you are under no contractual obligation to fulfil anything (but consult the lawyer), and can leave without giving them notice.

Now, you may find unethical to leave your students hanging like this, but the mere threat that you are willing to do it, may get some wheels spinning to give you a decent offer.

Another option to consider is whatever anti-slavery laws apply in your jurisdiction, since you are working for free; and anti fraud, because you are working without a contract. Furthermore, since you don't have a contract, you are not covered by the insurance, and if anything were to happen during your lecture, there is trouble. Think who would have to pay for in case, for example, a projector caught fire and ruined the classroom.

If your oral agreement is considered a contract, you can't do this; but then they would be acknowledging they have to abide by these rules.