Can't say I noticed, really, although Elnoyles are really useful things to kill as the items they drop are really good for modifying some weapons and making better items.

There is a soldier in Esthar after the Lunar Cry (although I can't for the life of me remember where... ), and if you talk to him, you will always face an Elnoyle. He'll disappear after the fight, but you can keep coming back to that screen, that soldier will always be there. That's about the only interesting thing I know about the Elnoyles.