There are no endentured servants in the United States so they can not force you to stay. You need to read your contract to see if you face any penalties for leaving before the contract is up.
I am a former federal and State prosecutor and have been handling criminal defense and personal injury cases for over 17 years. The above answer, and any follow up comments or emails, is for informational purposes only and not meant as legal advice.
One important question is your legal status for immigration purposes. Putting the immigration issue aside, all employment is "at will" unless there is a contractual agreement otherwise. Typically, only very highly paid executive have provisions for golden parachutes, etc.
Your contract cannot alter legal obligations of an employer to an employee.
Your employer is clearly acting illegally by not putting you "on the books". You may also have a fair labor standards act claim here. I strongly suggest you meet with an attorney as soon as possible.
Even with an employment contract the thirteenth amendment to the constitution has been interpreted to deny employers the right to compel you to stay in a position. This is the amendment that prohibits slavery. My colleagues have raised important issues regarding your status as a citizen, if you are not being paid properly you should file a complaint with the labor department or contact an employment attorney for advice.
Best of luck!
NO LEGAL ADVICE GIVEN. READ THIS BEFORE you contact me! My responses to questions on Avvo are never intended as legal advice and must not be relied upon as if they were legal advice. I give legal advice ONLY in the course of a formal attorney-client relationship set forth in a written document executed by the client and by me or a member of my firm. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. My law firm does NOT provide free consultations. Please do not call or write to me with a “few questions” that require me to analyze the specific facts of your history and your case. I can give advice, make recommendations and answer specific questions only after reviewing the evidence and documents applicable to a specific client and following a personal meeting in my office in which the relevant facts can be developed and analyzed. My law firm presently accepts cases involving State and federal administrative law; professional licenses and permits; education law; employment and labor law; and litigation matters in state and federal courts. Our practice is limited to the States of Oregon and California. If you have a case in any other state we would not be able to assist you. Unless we have a signed written fee agreement you are not my or my firm's client.
Without reviewing the contract it is difficult to give you useful advice. I recommend that you seek a private consultation with an employment lawyer. Many of us are willing to give free initial consultations. Good luck.
The information contained in this answer is attorney advertising and it is not intended that the recipient rely on this answer. Legal advice is only provided on the execution of an appropriate retainer agreement. This answer furnished by Holman Law, P.C. does not, by itself, create an attorney-client relationship between you and Holman Law.
You cannot be required to maintain employment. It sounds from the information that you have given that your employer is acting illegally, and that you have a potential lawsuit under the Fair Labor Standards Act. I recommend that you speak with an employment attorney in your area to determine your rights. If you cannot afford to speak with an attorney, I suggest that you contact Legal Aid; I suspect they would take your case.