Hey, I've been exactly where you are! Big ol' dog kennel, lots of runoff, mud, soggy wood chips, stink...
First, do away with the chips, straw, etc. It just soaks up water and holds it, making everything nastier.
Second, block water from coming in and speed water going out. Put logs or landscape timbers along the outside of the high sides to stop runoff entering. Clear along the inside of the low sides to help water run out through the wire. You can also spread a big tarp over the top - anchor it with bungee cords to trees or posts, so it overhangs the sides and blocks rain from blowing in.
Third, go out during a good rain to observe the water flow. Divert it around the coop - you can place logs at an angle where the water flows, or dig trenches to change the direction a bit.
Once you've done all that, evaluate the situation and see if you need to build french drains:
http://www.easydigging.com/Drainage/installation_french_drain.html
Also at this point, sand may become more useful.