That's interesting.
You say you don't have Elements nor Adobe Reader installed, but Photoshop CS5, Lightroom 3, a Flash player and Adobe AIR.
The only application we both had installed is Adobe AIR.
I suggest you do an EasyFind (see my previous post) search for Adobe AIR and delete everything associated with it.
Then see if you're still getting all those files. There should always be a few of them because the system needs them, but never more than about 10.
Apparently Adobe AIR is not essential for anything.
Please post back here to let me know if this solves the problem.