There is no such thing as an "odometer sensor." There is a vehicle speed sensor that is located on the output shaft housing of the transmission. That sends info to the speedometer. From there, the speedometer and the odometer are both operated internally, so if your speedo is working, but the odometer isn't, you have a problem inside the speedo head assembly.
Approx $70.00
Most likely a loose connection or bad sensor it is electronic
Six
You need to replace the speed sensor on the rear of the transmission.
how do I replace a parking lamp (left) on a 1996 Ford Taurus
The 1996 Ford Taurus heated oxygen sensor can be found behind the dashboard on the passenger side of the passenger compartment. The oxygen sensor should be labeled as such.
A 1996 Chrysler Town and Country does not have a speedometer or odometer cable. That signal comes from the transmission output speed sensor.
Check the speed sensor.
You cannot repair an O2 sensor. Replace it.
Speedometer is ran by electronic sensor on rear end. Odometer is ran from speedometer. If both don't work problem is sensor. If speedometer works sensor is okay. If speedometer works and odometer does not problem is in mechanical parts (gears) of of odometer and has to be replaced. Can get used from eBay (search for speedometer or odometer, is one unit) or take to dealer.
According to my Haynes repair manual, 1996 and later models do not use a conventional speedometer cable. They use an electronic speedometer and a vehicle speed sensor (VSS)
I had this exact problem on my 1996 Taurus. The solution in my case was to replace the transmission range sensor. I replaced it myself. It was easy to change. I can't say if that is what is wrong with your Taurus, but it was what was wrong with mine. Good Luck! This was also the problem with my '96 Taurus... part was also refferd to a Nuetral Safty Switch"