Hi dominica,
I'll take a stab at your question. First, let me ensure I understand what you have:
SpeakersMains - Polk VM30 Floorstanding
Center - Emotiva ERM-6.3
Surround - Emotiva ERD-1
Back Surround - Polk VM20
Front Wide - Emotiva UAW-8.2
AmpsEmotiva UPA-200 - new arrival / nothing connected
Emotiva UPA-500 - Front Wide L/R, Surround L/R
Emotiva UPA-500 - not in use / nothing connected
Onkyo TX-NR818 - Back Surround
Other unknown amplifier - Front L/R, Center? (or were these speakers previously connected to your Onkyo?)
There are many ways to skin this cat and I've listed a few options below. According to this
high-res image of the rear panel, your Onkyo has preouts for 7.2 channels, plus the optional Wide/Height channels. The additional Emotiva amps will allow you to move the Wide speakers off the Onkyo to the external amps.
OPTION #1UPA-200 - use for Main L/R
UPA-500 #1 - use for Surround L/R and Back Surround L/R
UPA-500 #2 - use for Center and Front Wide L/R
This option is probably the simplest and allows you to run the Front L/R speakers on a dedicated, high-performance amplifier. By utilizing both UPA-500 amps, you can power the rest of your speakers, including the Wides. You'll also have two extra channels available on UPA-500 #2, so you could use them for a Zone 2 setup or alternate, small 2 channel setup.
OPTION #2UPA-200 - use for Main L/R
UPA-500 #1 - use for Front Wide L, Surround L, and Back Surround L, and Center
UPA-500 #2 - use for Front Wide R, Surround R, and Back Surround R
This option provides the same dedicated amp for Front L/R, but uses each UPA-500 to power either the left or right side speakers. Notice that each UPA-500 powers one half (or side) of the system. You can maximize surround separation here between left channels and right channels. Of course, you'll still get two free channels available on UPA-500 #2 for a Zone 2 setup, etc.
OPTION #3UPA-500 #1 - use for Front L, Front Wide L, Surround L, and Back Surround L, and Center
UPA-500 #2 - use for Front R, Front Wide R, Surround R, and Back Surround R
UPA-200 - use in another system, sell, etc.
This is a variation on Option #2, except it removes the UPA-200 from the system and connects the Front L/R speakers to the UPA-500 amplifiers. Notice that each UPA-500 powers one half (or side) of the system. This is a great option to use if you can only fit two amplifiers into your setup, but want all the speakers connected to external amplifiers. It also provides the least "waste" of amp channels.
I could list a few other options, but these are the main three I'd consider. It comes down to how much space you have available for amplifiers, as well as overall preferences.