Most of the articles linked assume one is using paper strips and laying them up with glue. An alternative process, especially using newsprint is to actually "pulp" the paper and layup on a form in "gobs." For small projects, the pulp can be made in a kitchen blender, and for larger batches a bucket, and a "paint mixer" in an electric drill will get you there.

A difficulty with this latter method is getting consistent thickness as you lay it on; but there's little real difference in the end result for small objects I've made. For larger items the "strips" method may offer somewhat better strength, although I've never seen a test lab report on the structural properties of pâpier maché.

As dick greehhaus notes, going the bit extra and just doing it in fiberglass and resin will produce (depending on how well it's done) a much stronger case that in principle would protect your instrument better.

The method of laying up layers of strips or sheets with adhesive is quite versatile, and one way of getting slightly better strength than with paper would be to use cloth in place of the paper; and a cloth first layer and last layer with paper in between may give more durable exposed surfaces.

There are no water-base glues/pastes that will be truly waterproof after the job is done. Even the "outdoor" pvc carpenter glues are only "tolerant" for rain or other incidental moisture that runs off or evaporates fairly quickly without having a chance to soak in. Latex paints/enamels, and many varnishes are "moisture permeable" on purpose, so any prolonged exposure to moisture will let the paper inside get damp eventually. If you use a "coating" to exclude moisture it will eventually pick up enough chips and cracks to let the innards be damp. This is not to say that a serviceable instrument case can't be made; but you do need to recognize the limitations of the materials.

Experience many years ago with classroom art projects also suggests the warning that initial drying of pâpier maché projects should be done in an open area with free air circulation. Damp paper, especially with the common flour-based glues, can be incredibly susceptible to molds and mildew, and a project left in a closet for a couple of days may come out green and fuzzy. (Okay for long-hair musicians, I suppose, but who else wants a furry case?)

And don't forget about the termites and the bookworms.

John