You have way more issues than just the way you are getting paid. If I read this right you are working here ILLEGALLY and your employer is employing you ILLEGALLY. There's no such thing as an I-135 visa. You'll have to explain just what you are trying to accomplish there.
Do you actually have a SSN?
Anyhow, regardless of whether they take tax out (considering you an independent contractor, validly or not), you are responsible for paying taxes and yes the payer will need your SSN, as CBG says.
You should talk to an attorney before you continue to break the law and cause yourself further issues with the tax and immigration "man."

