I don't think EOs are illegal - just abused.
http://en.wikipedia.org/wiki/Executive_order
http://en.wikipedia.org/wiki/List_of_United_States_federal_executive_orders
http://en.wikipedia.org/wiki/Executive_order
US presidents have issued executive orders since 1789. Although there is no Constitutional provision or statute that explicitly permits executive orders, there is a vague grant of "executive power" given in Article II, Section 1, Clause 1 of the Constitution, and furthered by the declaration "take Care that the Laws be faithfully executed" made in Article II, Section 3, Clause 5. Most Executive Orders use these Constitutional reasonings as the authorization allowing for their issuance to be justified as part of the President's sworn duties,[2] the intent being to help direct officers of the US Executive carry out their delegated duties as well as the normal operations of the federal government: the consequence of failing to comply possibly being the removal from office.[3]
http://en.wikipedia.org/wiki/List_of_United_States_federal_executive_orders