Mitsubishi 82 inch big screen TV or projector?

I will not go into great deail on your projector question. I will let the pro's answer that. Although, I (me) would go with a low hour used projector. Possibly even stack 2. The 82" Mits doesn't stand a chance against a good line doubled projector.
My biggest concern is your room dimensions. Dude, Those are horrible dimensions you are talking about here, For the sound portion. Let alone only a 120" screen in a 22' wide room. You will need to break out the hammer and nails man and divide that room up correctly.
The proper dimensions are to be based on your ceiling height. Someone help me out here, it has been a while since I had to do the formula. Lets see, 20' high ceiling. Whew, I think it is X 1.3 for width, X 2.3 for lentgh. Is that right? You have some real problems here.
That is unless you just don't care what it sounds or looks like and just want to impress people. I suggest you find the proper formula and spend the money correctly. Measure once and cut it twice as the old saying goes. Maybe you could divide the room and have a nice entrance with the popcorn machine and that stuff. I wouls go 2 projectors stacked and at least a 18' wide screen. Maybe 4 rows of some cinema chairs. Hope you have a real good system to fill that room.
All in all though I wish I had ceilings that high when I built mine. Maybe you could put a basketball court in.

If you plan on sitting more than 9' from the set or want multiple rows of seating you'll want a screen bigger than 82" diagonal. Probably much bigger.

Beyond 13' even a 120" diagonal 16:9 screen is going to start getting small. I'd consider it too small for home theater use beyond 17' and marginal well before that.

Attempting to get 120" diagonal at both 4:3 (96x72") and 16:9 (105x59") will be difficult and either produce a 4:3 image that's too big or wide screen images that are too small. A 59" high screen screen is a better idea (4:3 will be 79x59 for 98" diagonal) assuming 105" is the appropriate width for you (people's sensitivity to source/projection artifacts varies), your projector (which determines the sorts of projection artifacts you'll have), and your seating distance.

You really need to start playing with projectors and seeing what subtended fields of vision work for you.

This will not be a dedicated room for home theater. My living room will have to be incorporated with the screen and projector. The screen will have to go against the long wall...so the maximum throw for the projector will be 14 to 18 feet. Even though the room has crazy dimensions....I've got the sound system pretty well dialed in..my system is below

Amplifier: (4) Carver Silver 9t monoblocks
Preamplifier Audio Research LS-10
front Speakers: Infinity Kappa 9 (bi-amped, 2 monoblocks per speaker)
Sources:
CD Player: Carver 360A 5 disc changer
Turntable/Phono Stage: Oracle Delphi Mk1 phono

Grado Platinum cartridge

Carver C-19 Vacuum Tube Reference preamp for phono stage only. My main preamp does not have a phono stage.

Other Source(s): Sansui TU-X1 tuner

Otari MX-5050 Reel to Reel

Other Accessories/Room/Misc.:
Speaker Cables/Interconnects: Radio Shack Gold Cable Interconnects

Home Depot 12 gauge speaker wire

Room Size (LxWxH): 70 ft x 22 ft x 20 ft
Room Comments/Treatments: My living space is a loft that was converted from an old beer brewery. I've filled it with furniture and carpeted it.
Music Preferences and Comments:
Music Used (Genre/Selections): jazz
System Goals/Comments: upgrade the cables and maybe try a tube preamp, maybe an Audio Research Reference 1 or 2
System Strengths: I like the way it sounds
System Weaknesses: interconnects and speaker cables

Video/HT System: Integrated
TV/Projector: Phillips 61 inch bigscreen TV
Processor/Amplifiers: Sunfire Theater Grand II processor

(2) Sunfire Signature stereo amps for rears

(1) Carver TFM-45 stereo amp for center

Speakers (Center, Surrounds, Sub): Center: Infinity Kappa center series II

Rears: (2) Infinity Kappa 9 (bi-amped)

Sources (DVD/VCR): Samsung DVD player

Atari Jaguar game console

Nintendo Game Cube

Other HT Gear: Radio Shack Hi Fi VCR
Comments on HT System: sounds outstanding, adding a subwoofer may be overkill

I did read the test on that tv. It wasn't much. Like they just repeated info from the sales info sheet. A 92 diag is what I have.--That will be 'small' in your room. I have the newest Sim 300extra h. There is a new Sony just about to hit the streets viola or something like that. 25k, and it does 1080/1920. That has to be the way to go. My projector image is much better than you see at your local cineplex. The Sony must be better than that of the IMAX.