PVC is the same material that is used for plastic pipe. Yes, MEK and acetone will soften it and may work. I would still use the solvent that is sold for it. This is solvent welding and is quite strong. I use PVC and CPVC rods, sheet, and pipe for all sort of projects. PVC does not support weight very well.
Polystyrene is what was/is used widely in scale model airplanes, tanks, etc. Most hobby shops will have a water-thin and a thickened version of "adhesive" for plastic models. Both actually produce a solvent weld too, are quite strong, and I suspect they will work for both polystyrene and PVC. However, I have never used it for PVC, because the stuff sold specifically for PVC and CPVC works so well and is inexpensive.
ABS -- This is a bit more difficult to solvent weld or to make adhere with an adhesive, but is still quite easy compared to the really difficult plastics. It is stronger than PVC for supporting weight. An adhesive/welding solvent made from chips of ABS dissolved in methyl ethyl ketone (MEK) is even recommended for repairing interior parts of some full scale aircraft. Acetone will probably work, but MEK is less volatile and a little easier to work with.
For your siding and boxes, you may want to take a closer look at Coroplast. It is extremely durable and the corrugation gives it a special look you will learn to love. It is available in various colors; white is most common. It is getting used more and more in consumer markets. I have seen garment storage boxes made from it at home stores. I use duct tape (really) or gaffers tape (very similar) to hold my boxes together. A two-part flexible adhesive will also work. I use an acrylic, as mentioned above, but it would be worth trying a polyurethane ( e.g., Gorilla glue) available in home stores. It is so impermeable to water that you will need to mist one surface first before assembly. As for price, it is really cheap. I pay about $8 per 4X8 ft sheet at an industrial supply for packaging. Craft stores sell it for several times that amount per sq ft, but it is still relatively cheap compared to ABS.
John