I swapped the rear axle in my 1990 Volvo 240 wagon with the rear axle from a 1993 Volvo 240 wagon. After that, the speedometer was incorrect and would jump around while driving, even when I replaced the gauge cluster with the one from the 93 wagon. I tried looking online but couldn't find much. Any advice? I heard it may be because the rear running gear has more teeth or whatever.

 

"Jump around" should not be the result of a different gearing. That would produce higher or lower speed readings. Sounds like you are having the dreaded electronic issues for which the 240s are famous.

 

The '93 tone ring in the differential has more slots than the '90 and will cause incorrect readings in the speedometer/odometer. You will need to use the '93 speedometer. As far as the needle "jumping around", make sure all electrical connections are good.

A good resource for troubleshooting speedometers can be found here:

Electronic Speedometer Notes

 

@act1292 I did swap the 1993 speedometer over so I will check all connections and read your link