Welcome to Fluther, first of all.
Before I answer your question, let me say that “the answer hardly matters”. That may sound harsh and unhelpful, but I think it’s probably the truth here. That is, if you don’t have “the funding” to move out of the house, how are you going to engage the services of an attorney to mount a case against your parents, assuming that what they have done (or threatened to do) is actionable at law, i.e. “illegal”?
If you’re living at home and using your parents’ car, then you’d better quash such notions of strict “legality” (assuming that your basic rights are respected) and follow the rules that they set for you to live in their home and use their car.
If you want to stand on fine points of law, they could also make a case that your use of their car outside of the agreement you had made with them to use it in a certain way was also “illegal”. And there’s a name for that kind of illegality; it’s called “car theft”. No, I don’t think you want to do that dance with them and actually get thrown out of the house, do you? (That would also be “legal” in many jurisdictions, and in nearly all US jurisdictions after you were given sufficient notice.)
But to get back to answering your specific question: No, it’s probably not technically legal for your parents to throw away your possessions, and almost certainly not legal for them to confiscate your paycheck. (It is completely illegal for them to intercept your mail, if that’s how your paycheck is sent to you.)
But… don’t make a federal case out of this. Really.
You should:
1. Apologize for breaking rules that you had apparently agreed to.
2. Promise to make right the damages you have caused – because insurance doesn’t cover everything, and may not cover the damage done to their car if they don’t have full coverage, and may have a high deductible in any case. (You need to learn these things.)
3. Make good on the promise.
4. Get your shit together and grow up, and then move out.
Some of that may also sound harsh and offensive, but it’s said with the best will and intention in the world. The best thing that you can do now is to grow up.