I'm a restaurant facilities manager, and so I have seen many dozens of similar problems. A foul smell like this is almost always related to the plumbing system. (I am guessing that you don't continuously have animals dying under your house - seems like you've already checked that.) If you've not already checked these areas, here's what I'd suspect:
1) Find the fresh air intake on your heating system. Now, is there a floor drain nearby? If so, pour water into it (about a gallon should do). Sometimes the p-trap in a floor drain will dry out, and so sewer gas is able to escape into the air that you breathe. It smells terrible, but fortunately it's a very easy fix!
2) If there is no floor drain, is there a hand sink, laundry sink, mop sink nearby? Check to be sure there has been water poured down those drains recently too.
3) If none of the above applies, is there a toilet nearby? Replacing the wax ring under the toilet may solve your issue (or sometimes 2 wax rings are needed, but only 1 has been installed - again, an avenue for sewer gas). If not, see if there is a plumbing vent pipe running through the wall. If so, it may have a crack in it - this would also allow sewer gas into the air.
4) Last resort, have the sewer lines in the area video'ed by a plumber. There may be a crack or hole in one of the sewer pipes. This is actually fairly common in homes of a certain age (and/or if bleach or drain-o has been used a lot). If there is a hole in one of your sewer pipes, I would check out a Trenchless plumbing company - yes, it's a bit more expensive up front, but you will have NO damage to the floors/walls in your home, so in the long run it's cheaper. I have used trenchless plumbing repair many times with great success.
5) If nothing above works, then you may have mold/mildew growing inside one of the adjacent walls. If this is the case, you'd be able to see it - the walls would feel squishy and would smell awful. I promise this is not as scary and expensive as you probably imagine. All you need is a good GC with experience in this area - they can safely remove any affected drywall, fix whatever's leaking inside the wall, and close everything back up. (We do this ALL the time in restaurants - typically for us it's an overnight job.)
I hope these suggestions help. If you need any contractor recommendations, let me know! I have managed maintenance and construction all over the state so I have a pretty big list of good contractors if you need it.