I am obviously not from your area so take any advice I offer with that in mind.
Educate yourself on what the fair market value is by looking at recent comparable solds. Banks are looking very much at the bottom line and the idea that there are REO properties in move-in condition that are great deals is somewhat false. Sometimes a fixer-upper (which MANY REO properties are) can be had for a good price.
If an REO's asking price is considerably below fair market value then it is often listed with the intention of encouraging bidding wars. Unfortunately, this is sometimes a successful strategy.
If an REO's asking price is listed at fair market value, then treat it the way you would any other property: offer what its worth to you.
There is no set percentage to offer below asking price. It all depends on condition of property, how well its priced and ultimately what it is worth to you.