The AEO Handbook has moved its location on the Web again and can be found now at:http://www.communities.gov.uk/publications/localgovernment/attachmentordersemployers
Your payroll software may help with prioritisation once they are all entered into the system. What you should be doing is applying them in date order, as they all have equal priority. You make the appropriate deduction under the earliest dated Order, which recalculates their attachable pay. If there is sufficient pay after the deduction has been made, you apply the next Order, which again recalculates the attachable pay. If there is enough attachable pay remaining after this, you can apply the Order with the latest date on it.
In short, if the employee has enough pay, you would be able to apply all three Orders. The problem that you would have is if all three were CTAEOs, in which case you could only take the earliest two.
Will your payroll software help in this regard?