From my research, denim (or other insulation-type material) doesn't do much for sound deadening, but it does provide thermal insulation. It will help with sound slightly, but that's not it's intended use. I think this whole thing can fall into two categories:
1) Sound Deadening
Here are some resources on sound deadening:
Australian guy who owns a professional car sound deadening shop (video)
A simple YouTube search on how to sound deaden cars (notice how everyone uses the same material)
The first video does a great job showing how sound deadening material will reduce and eliminate frequency resonance, thus reducing and eliminating sound. Everyone seems to use this rubber-like material which has a foil/shiny side and a sticky/adhesive side. It's applied with a roller, and some reviews recommending using a heat gun to promote better adhesion. Graffing tape is also used to tape any lose cords as these can causes rattling. This sound deadening material can be applied to anything that is metal. Alex has a great picture above showing his gutted car. All the metal you see can be sound deadened. Be sure to sound deadened the doors as well, and the roof if you're ambitious.
Here are some products I found:
Noico - 80 mil thickness, 36 sqft - $65.99
Killmat - 80 mil thickness, 36 sqft - $57.99
Kilmat - 50 mil thickness, 50 sqft - $59.99
Rolling wheel - $9.99
(probably any sturdy polyurethane roller will do fine, but keep in mind a smaller size will allow you to get into corners and nooks)
Gaffing tape - $16.98
The sound deadening material linked above is much, much cheaper than the name-brand equivalents. Being that we are talking about sound deadening a Mirage, save your money. Reviewers report a big sound difference in using these cheaper products.
2) Thermal Insulation
I'm still researching thermal insulation. I will update this post later when I have more info. I do plan on gutting my Mirage and sound deadening as well as possibly throwing in some thermal insulation (I live in Wisconsin, it would be a benefit for me).
It seems like stuffing the car doors with denim is a really good solution, because there is a lot of extra space between the metal door and plastic interior. This extra space acts like a speaker and will amplify sounds. However, I'm not sure about using denim in the rest of the car. I worry about liquids being absorbed into the denim, and causing mold and smell issues. Alex does cover some of his denim with plastic, which is a great solution. If I were to insulate the car (not just the doors) with denim, I would definitely layer everything with plastic and not just some pieces.
There are some other products that sit between the sound deadening material and the carpet. These are called "carpet underlay". This material is waterproof, so anything spilled on the car carpet will not be absorbed into the carpet underlay. Here is a quick resource on these. And a video from the same Australian guy. These seem to get pricy, so I'm undecided as to whether or not I will be adding these in addition to the sound deadening.
Hopefully this month I will find time to install sound deadening throughout the entire car, as well as installing some denim insulation in the doors. Whenever I get around to it I will take photos, possibly a video, and make a new thread. Maybe it will be a "how-to" type of thing.