My son works on average over 40 hours a week.He works in a hospital in NJ. He does receive overetime when he works over 40 Hours. However he is considered a part time employee and they will not give him a full time listed position even though most of the time he works 40 hours or more.
There fore he is not entitled to any benefits such as health insurance, vacation pay etc.
Is this legal. He has been working there about 3 years.

Hospitals employ part-time, full-time, and PRN people. While any one of these can work 40+ hours a week, it is only the employee who is on the payroll as a full-time employee who gets the benefits.

He will have to talk to HR to see if he can get his status changed from part-time to full-time.