Sorry Kevin - you do have a couple of issues. Here's some thoughts:
It would be most helpful to know what is taking the eggs. The best solution is to set up a camcorder but that's expensive. A much less expensive way to find out is to spread something like flour evenly across the floor so that the stealer has to walk through it leaving it's tracks. You could also use a thin layer of mud if it's somewhere you can clean it up easily and it won't dry out quickly.
Once you figure out who the culprit is you can then make your plan of attack or capture.
If the above doesn't work then I would suggest some type of wild animal trap and try different baits to see if you can catch something.
As for mice, a good barn kitty is always a great solution (if you can have one there or want one). Also mice are drawn to food that is dropped either by you or the chickens so keeping things scrupulously clean is one of the keys. Your feed should be in rodent proof containers - that usually means something metal. I keep mine in five gallon plastic buckets and have never had a problem ... but we have five barn kitties that patrol our property also.
Try to make sure there are no holes anywhere (even a tiny hole is an invitation to a mouse) in your hen house and food storage area. You can fill holes in with steel wool, mice will seldom get through that or sheets of metal.
I wouldn't suggest using mouse poison unless you are absolutely positive no other animal or child can get to it. Mice traps can work very well using cheese or peanut butter ... you can use live capture or kill traps depending on how you feel about it.
If your coop is up off the ground a few inches the mice could be living underneath it, or they could have dug under it. I buried wire down about 12-18 inches around my hen house and stapled it to the side of the wood. Keep all debris like grass and weeds cut really short around the hen house and don't let piles of wood or anything lay around as mice love to hide in those.
Good luck, hope some of these ideas are helpful.
