If I agree to not work for overtime, is it legal for the employer to pay just the standard rate?

Employees may NOT give up their right to overtime. If you are a nonexempt employee (that is, someone who would normally be entitled to overtime, which includes all hourly employees), then you MUST be paid overtime if you work more than 40 hours per week. The only legal way to control overtime is for an employer to not require or allow employees to work more than 40 hours; but if they do work more than 40 hours, all hours over 40 must be at overtime rates for nonexempt employees. If you are not paid for overtime when you should be, you could either file a complaint with the labor department or sue for the money you are owed.

If you are exempt from overtime, of course (and many salaried staff are), then you do not receive additional compensation for working more than 40 hours in a week.