My company decided to do away with my position, but gave me another position within the organization a yr ago. Now the company is looking to hire for my old position. Are they allowed to do that or do they have to allow me to apply for my old position?

If you agreed to move to a new position a year ago the company can re-hire for your old position and doesn’t have a legal obligation to hire you for the old position. If you want your old position you should definitely express your interest in applying.