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.

I beg to differ with the last couple of responses. If you'd really like to get the best sound possible from your setup, you really need to make an attempt to gain a solid understanding of how your gear, room acoustics, speaker placement and seating placement are interacting.

Get a cheap spl meter from Radio Shack and a cd with test tones from either rives.com, a website or a Stereophile test cd. Place the meter on a camera tripod where your head is when you sit in the sweetspot. Measure the response using the test tones (search archives here on how to do this exactly), and graph them on the chart you can download from rives.com.

If you play with speaker and seating placement & remeasure, you will be able to significantly affect in room bass performance. Often you will have peaks at some frequencies and troughs at other frequencies. Offer, you have to live with tradeoffs to get the best overall balance. Bass traps in the corners behind the speakers offer the biggest improvement in most situations. the room acoustics forum on audioasylum is the best place I've read up on this topic.
Good room treatment doesn't have to cost tons or look like hell. Natural fibre rugs, velvet curtains, upholstery and bookshelves can all contribute to improved sonics if diy or commercial room treatments aren't in your budget or to your liking.
Don't let anybody fool you. The room is probably your most important component. Cheers,

Spencer