You don't need to wash or refrigerate your eggs.
In fact, it's better to do neither.
Chickens naturally coat each egg with a protective layer as they are laid, called a 'bloom', which protects the eggs from bacteria. If you wash the eggs you remove this protective coating. Also, eggs are designed to not spoil for several months in the wild, without refrigeration. Just wipe off any poop with a slightly damp paper towel, and keep 'em on the counter in a nice little basket for easy display.
Here in America we have this bizarre obsession with sterilization and preservation. In Europe, most people keep eggs(and butter) on the counter, not in the fridge.
Personally, I have chosen my hens to produce a colorful basket(brown, dark brown, blue, and green), and I want to see those pretty little eggs! Why hide them in the fridge?
For me washing the eggs is well, just essential. For the most part our eggs look pretty clean when we collect them. But, to risk possible chicken poop getting into my morning fried eggs washing them is a must. I am kind of a bacteria freak though
I don't wash the eggs, unless one is really dirty, then I only wash it just before using. I have explained the egg coating to those that purchase my eggs and they do the same. I do refrigerate, though sometimes not until the next day, I know its not necessary, I just do it because I have a big dog that sometimes likes to get on the counter....
I am so pleased you asked that question - i read somewhere recently that they MUST be washed but I never have in the past...after reading that I sometimes did a half hearted run under the tap but my girls mostly lay such clean looking eggs...obviously if they are dirty then yes, I will clean them. Most relieved!! No need to send out instructions to everyone I have given eggs to!
All of my eggs get washed and refrigerated. I'm not putting anything with manure on it inside of my fridge.
Whether you should refrigerate or not depends on your own personal preferences. I sell eggs so I want them to maintain their quality for as long as possible. A day warm kitchen counter is about the equivalent to a week in a refrigerator so far as maintaining a firm yolk and thick white are concerned.
I don't ordinarily sanitize my eggs unless I'm going to hatch them.