My son has shown me a trick -- If I need to CLEAN a tension (not a machine that has been sitting a long time without use), I sew a chain on my serger and use that to clean the tension. It has worked very well on frequently-used machines. HOWEVER, if I had a machine that had been sitting unused for an extended period of time, by all means take it apart and clean it thoroughly. Tammi and Miriam are the experts on tension assemblies. Also, just a reminder, when you take something apart, take photos as you go, giving you a picture as to how you need to reinstall every part. Don't hesitate to use parts containers -- parts can get misplaced, or screws dropped and they're by far harder to find than you might think!
Jeanette