How to diagnose the need for room treatment?

Given that none of your dimensions are evenly divisible into any other: You're ahead of the game. Here's a possibility, as far as an available test that will help you in identifying problem areas- (http://www.acousticsciences.com/matt-test-flyer.pdf) The test is available on Stereophile's Test CD 2: (http://ssl.blueearth.net/primedia/home.php?cat=2) The other test CDs that they offer have some good listening room diagnostic tracks as well(that don't require any instrumentation, outside of your ears). ASC's site (http://www.asc-hifi.com/) offers much in the way of explanation, re: resonanaces, echo, reflections, reverb, comb filtering, etc., and ways to treat a room to combat/control them(click on, "Acoustic Basics"). Auralex(my fav) in it's many forms(and a number of other treatments) can be purchased very reasonably on eBay (http://shop.ebay.com/?_from=R40&_trksid=m38&_nkw=acoustic+foam&_sacat=See-All-Categories) (http://shop.ebay.com/items/?_nkw=acoustic+treatment&_sacat=0&_fromfsb=&_trksid=m270.l1313&_odkw=acoustic+foam&_osacat=0) Hopefully you'll find something in this short list of resources helpful to you.

Try playing something that should have lots of bass. If your system should be able to play deep bass and you can hear it, and are happy with it, you are probably be OK.

If the bass is lacking or muddled, you may need bass treatments in the corners of your room.

You've played with speaker position and you've dealt with the first reflection points (including floor bounce?) and in your opinion it sounds good. If that's the case, then don't go any further. It's not that you couldn't improve the sound quality, but go to the above websites graciously listed by Rodman and look at the products they offer. Then ask yourself whether you really want them in your living room? I suspect the answer will be self-evident.