Well, if it's a rodent, if it got in it can probably get back out again. Which means that it can get back in again. The first thing to do is to figure out whether it can get out of the walls. If it can, it's easy enough to trap it. Look for droppings, hair, footprints, etc. Put out some bait and see if the bait disappears.
Otherwise, you could try to figure out how it got in. There are a million and one ways for a mouse to get into a house, and it's somewhat harder for a rat to get in. Of course, most entry points are at ground level. If you have a solid foundation to your home, that'll cut down on vectors, but if your house is hollow underneath, as I'm led to believe many American homes are, that could be a problem.
The good thing is that a rodent is unlikely to starve and die in a wall, since it can probably escape on its own. The other good thing is that if it does die, sheetrock absorbs moisture quickly so it will probably mummify the citter pretty quickly, preventing much of the stink. Not much moisture in a mouse anyway.