No Social Security Numbers and Benefits for Illegal Aliens Act of 2014 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act to prohibit the Commissioner of Social Security from assigning a Social Security account number to any individual who, according to the Secretary of Homeland Security (DHS), has been authorized to be employed in the United States in accordance with a certain DHS memorandum dated November 20, 2014, and who would not be so authorized but for that memorandum.

Prohibits the payment of OASDI benefits to such individuals.

Denies the crediting of quarters of coverage toward benefits for earnings from unauthorized work by an individual who is not a U.S. citizen or national and who was not authorized to be employed in the United States.

Prohibits counting an individual's annual wages or self-employment income for any year for which no quarter of coverage may be credited.

Directs the Commissioner and the Secretary to enter into an agreement to establish a system to transmit to the Secretary any Social Security account number assigned to an individual after the enactment of this Act, as well as other identifying information, in any case in which the individual is not a U.S. citizen or national at the time that number is assigned.