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.

If you have a significant-other's-acceptance issue. There are very attractive alternatives to the pro-sound booth type traps/treatments. Some of which actually allow you to submit your own artwork/photographs for display, while still effectively controlling your room's acoustics: (http://www.asc-hifi.com/panel-trap.htm) (http://www.purewaveaudio.com/c=bdYyIFF0rsQhnkyyRIpP7ioV5/product/AUR-SPS23/Auralex_24x36x1_SonicPrint_Panel_Uses_Movie_Art_Image_from_Auralex.html) Of course- How far you pursue excellence in your listening room depends solely on how serious you are about your music.