Monkeycustard, (I like that name!!!!)
Ahh, I thought (silly me) that you were running plain ol' Windows 98 (no SE). Well, I know that on my other computer (has Win 98SE and dual boot with XP) there is an important update to Win98SE which is known as the shut-down patch (available on Microsoft's update website). It's imparative to get that patch in order for avast! to shut-down properly -- in conjunction with the GracefulRpcShutidown=1 line added under the [AAVM] section of the avast data file known as: avast4.ini
It is located in the following path:
C:\Program Files\Alwil Software\Avast4\DATA
I know for sure, based on my personal experiences that avast! should work perfectly fine either with Windows 98 and 98SE. If it doesn't then there must be something else wrong with your system causing it to hang on shut-down.