It all depends on how much money you want to spend. Most amplifiers will have a Speaker Level (tapped right off of the oem speakers) input, in which case you don't need a Line out converter (LOC) Some amplifiers on the other hand, do not. There are also specialty LOCs that restore (or attempt to) any oem signal processing. But because you have a factory subwoofer that may not be necessary. (plus those LOCs are like $200-500, ouch!)
Something like this does the whole deal in one package:
http://www.crutchfield.com/s_108BASS...nk.html?tp=114
But I dare say if you already the JBL system in the avalon its probably not much better adding something like that Infininty BassLink, I have a Tahoe with similar oem equipped Bose system and that hits pretty hard.
Otherwise you will need a few components which I made a drawing representing hookup
Line out converter, you can just tie the two speaker level inputs together in parallel so it can handle 160WRMS
http://www.crutchfield.com/p_142LOC8...tml?search=loc
Then you need to have an amplifier hooked up, Id imagine it would be in the range of 500-1000W if you want to overcome the factory system by a noticeable amount. This will require 4 gauge wiring to the battery and a 100A fuse.
EQs and crossovers are not nessicary, because the signal will already be crossovered for the factory subwoofer
Once its all hooked up I would recommend detaching the factory sub woofer. (or leave it attached, its all preference)