How to tell if Acoustic Treatment is Needed?

Thank you for all the wonderful suggestions and links. With the speakers on the long wall I can't move my seating position or I'll be sitting on top of them, but it is something I will keep in mind for the future should I change the speakers' position. At present I think I'll try some diffusion on the wall behind my head.

What I think you'll need is, absorption on the wall behind your head.

Ken in Calgary - it's Kevin in Toronto here.

Some more thoughts for you:
(1) Get your hearing tested. Men, moreso than women, and especially after 50, lose our hearing quicker. Best to know if or at what frequencies you may be challenged by. If it's mid/high frequencies then all the diffusion and mid/high absorption won't mean a damn thing if you can't hear it to begin with. Sorry for the frankness.
(2) assuming (1) above is fine, in your case the first surface to deal with is the wall behind your head. DO NOT put diffusion there as you need to sit 6-10feet away from diffusion for it to work properly. I have both 1-dimensional GIK D1 diffusers and 2-dimensional Sklyine diffusers and you can sit closer to the 2-D because about half the sound is diffracted horizontally back towards you, but I digress. Instead, put some broadband absorption 4" to 8" thick sold by GIK or RealTraps, which means moving the picture to another wall. If you can't/won't move the picture, then try moving the bottom of the picture out away from the wall by putting a block of wood between the wall and the picture so that sound hitting the picture will be reflected upwards towards your slanted ceiling which will then be reflected down and toward your front wall (behind the speakers) which is fine.
(3) put a blanket overtop of your coffee table or move it during listening sessions so as to prevent high frequency reflections that interfere with the speaker's direct sound.
(4) try diffusion on your front wall behind the speakers.

No side wall treatments needed if your stereo is centered along the long wall.
No ceiling treatment needed unless by using a mirror you can see the tweeters from your listening chair in which case put up some diffusion (1D or 2D) if sufficent distance exists.

Generally speaking, think of your room in frequency bands and treat each one individually.
(A) Bass below the Schoeder frequency which in most rooms is about 300Hz: The clustering of bass nodes are less dense than upper frequencies which causes bass peaks and dips in SPL to be much easier to hear, so evening them out is the goal. Try to minimize the dips as best you can using absorption as the peaks can always be cut in volume with a little parametric EQ. Use 8" or more of absorption (diffusion would require well depths of several feet, clearly not an option) so to the extent you want or need better bass try putting bass traps in a variety of places, play some test tones and using a SPL meter graph the results. This is an iterative and time consuming exercise, so beware.
(B)Mid - Upper frequencies: for music you want to maintain the aliveness of the room to help create the "spaciousness" that is critical. Most domestic rooms are overly damped to begin with (i.e. furniture, draps, carpeting, people, pets etc)so I'd recommend diffusion over mid/high frequency absorption. Other main factors to consider are "timbre" and "location of instruments in space." All three factors will benefit from diffusion BUT only if you're sitting far enough away from it. This is why small room acoustics is so much more challenging than larger rooms due to more constraints. The deeper the well depths of the diffuser the lower the frequency it will work down to. The well depth is half the frequency wavelength distance and may in fact continue to work down one additional octave but less effectively.

So in summary, check your hearing, move the painting and replace it with 4"-8" absorption, move the coffee table or throw a blanket over it and pour yourself a libation. Enjoy and do report back to us how you made out.