Video: Learn How to Keep Mosquitoes Out of Your Yard
You have a lot of questions. I will try to cover them all.
First, mice can fit through a hole the size of a dime.
Second, unlike rats, mice are very small; it would take a major infestation to generate a persistent odor as indicated.
Elimination starts by sealing the exterior foundation of the home, door sweeps, broken windows, cracks in the foundation, holes around electrical service, water faucets and dryer vents.
Secondly, food sources must be eliminated. Mice only need 1 gram of food a day and they extract water directly from the food they digest.
Next, mice infestations are more localized than people think, bait under the house might not have any effect. Heat sources like refrigerators and hot water heaters are suspect as a base of operation.
Snap traps are highly effective when used where dropping are found. Use a variety of bait, peanut butter (avoid this if children are present), brownie, fruit and even dental floss tied to the pedal (nesting material).
As for the odor, look for an enzyme based cleaner / deodorizer.
If the problem continues seek the help of a Pest Control Professional with rodent experience.
Hope that helps,