Even tho eggs have cholesterol, there's very little proof that they contribute to blood cholesterol levels. What seems to contribute most of all is red meat.
Eggs are a very clean protein because they contain lots and lots of lecithin, which means they have lots of linoleic (sp?) and linolenic acids, which help to dissolve fats and take them out of the bloodstream. The whites, albumin, is very close to the albumin that runs through our bloodstreams as a transport mechanism for good things.
Yogis in India have done limited diets with 8-12 eggs consumed daily with no problem.
If you do have high cholesterol (anything over 180) then start taking cold pressed flax seed oil in addition to lecithin and it should come right down. :)
Go ahead and use olive oil with your eggs. Eggs cook at quite low temperatures so it doesn't hurt the olive oil hardly at all. If you're a Vata like me you can use butter too. :)