Do you mean executive orders which, in and of themselves, have continued to be in effect, or do you mean executive orders whose effects continue to exist? Examples of the latter might be the racial integration of the US Armed Forces or the foundation of the Peace Corps.

Additional question: Were the positions of cabinet officers established by executive order?

Here's a question if a law is unable to be found online, such as those prior to 1937, where would one go to find in any law books, is it still in effect?

There's this one by Jackson concerning disability payments in 1829.

http://www.presidency.ucsb.edu/ws/index.php?pid=67088

I think it's a good candidate if this is the procedure still used.