There are soundproofing curtains and soundproofing panels that can be found through an internet search for soundproofing curtains.
They are not cheap, window curtains starting in the $300 range for an average size window (and yours are much larger). Panels start at about $200 for a 4x8 foot unit and they still need to be hung on some sort of frame. Preframed versions are a good bit more.
Many people swear by white noise machines, but not all people find them effective.
Here's an out of the box idea. How about active noise cancellation? put a few decent quality full range speakers in the room and find some noise-cancellation software or circuitry that you can tie in with a couple of mics that you orient toward the worst of the sound, and tune the system to cancel out external noise.
If that doesn't sound appealing:
Here's an interesting article: http://www.soundonsound.com/sos/may08/articles/soundproofing.htm
The first answer suggests "alaska pack" wall construction, which would be great but maybe you can't go quite that far.
You might be able to fir the existing walls out and fill the gap with a dense material. Sand is actually a very good sound insulator because it is very dense, and because a lot of energy is absorbed by friction between the sand grains. You could build a false floor the same way.
Do bear in mind that the sand will be very heavy. You should calculate the weight and maybe get an engineer involved in doing a bit of math to make sure the existing structure can take it.
If you build the panels out with 3/4" plywood and secure everything well enough to the existing framing (or are your walls masonry?), you might be able to build it in stages, against the wall, seal all the joints extremely well with something like caulk or spray foam, and pour sand into it, do the next layer, fill that with sand, etc. Then put in an acoustic drop ceiling like the first answer suggests.
You could maybe use spray foam instead of sand to fill the gap, but it won't absorb sound as well because it is nowhere near as dense. In that vein, though, you could also try gluing solid foam panels to your existing walls.
Low frequency sound (trucks on the freeway) will be the toughest to block. Low enough frequency sound travels right though the earth itself, so good luck with that.
Electrical outlets could be a problem. You can't hide any electrical junctions, so you would need to use some kind of extension boxes to pull them out to the new wall surface.
Good luck!
Best Answer
Every 3db is double the power of the signal (amplitude), however this is also the point at which most humans report hearing a noticeable difference. Most humans will perceive the volume to double around 9-10dB.
So if you found one door that offered 30dB of noise isolation, and another that offered 40dB, you would say that the 40dB is "twice as quiet as the 30dB", approximately.
In reality, your sensitivity to sound is not linear so it really depends on the frequency of the noise. You are less sensitive at the high/low extremes and most sensitive in the center of the range. Likewise, as you get older, you tend to lose sensitivity to the extreme frequencies first.