Originally Posted by Frasier

removing the dates is something best done by hand, there are a couple plugin's out there that claim they can do it, but it really depends on your theme if they are successful or not.

A quick google on 'remove wp date/time' should give you some pretty step by step directions on how to edit the php loop to remove them. I was able to do this, so I'm sure you can too

There is a plugin called 'oldest to newest' that does exactly what it claims to do, but there is no randomization in it.

If you find a random post updater, let us know