There is no common connection there. The odometer is mechanical and is driven by the speedometer cable which links the speedo to the transmission. If the speedo is also not working then it could very likely be the cable - they go out on occasion. If the speedo is working then there is probably something broken inside the instrument cluster.

The gas gauge and temp gauge both use a reduced voltage supplied by a little relay-looking gadget that briefly supplies straight 12 volts when the key is first switched on to make the gauges jump up - then a reduced voltage that lets them respond sluggishly to sensor changes (I guess they didn't like seeing the real time sloshes on the older style gauges). If the temp gauge works then it rules that out. Other than that there is the gauge itself, a wire from the dash cluster to the fuel tank, and the tank sender. Try briefly gounding the wire at the tank and see if the gauge responds. If it does - deeply suspect that sender.