I actually commuted from Andover to Worcester myself, but that was over 10 years ago, and during typical am/pm commute times. Rt.495 (then Rt.290) is really your best bet from Andover. It was long, and often busy on some stretches, but certainly not nearly as bad as Rt.93 or Rt.95/128 can be (the Turnpike is further south, so you wouldn't do that from Andover anyway).
I also used to take a little known-detour for the latter part of the trip, taking Rt.2W from 495 to Rt.190S, right into Worcester ... this stretch was much easier and quieter - and more scenic - than Rt.495/290. If you're going to Worc. mid-pm though, I don't expect you'll have typical rush-hour traffic issues.
Hope that helps. By the way, I'm a REALTOR in Andover ... feel free to contact me if I can ever be of assistance, email@example.com. Good luck!... more