Styrofoam + gesso alone is far too weak for anything beyond a quick throwaway prop.
For something slightly stronger, I'm a fan of Smooth-On's Shell Shock. No odor, fast cure, and it doesn't eat through the foam, so you can just brush it on directly. Ya gotta order it online though, and it isn't the cheapest product around.
For real strength, you've got to use some sort of composite; a combination of a fibrous material and a resinous material. On the weaker end you've got things like paper mache or muslin+white glue, on the stronger end you've got things like fiberglass + polyester or epoxy resin.
After you have that nice strong layer that holds your piece together, you need a layer above that which can be smoothed. The fibers in the composite layer make it too annoying to just sand smooth. You can sorta get away with it in paper mache, but even that tends to get all weird and fuzzy on you.
A lot of products work as this smoothing layer, jointing compound, wood putty, spackle, paper clay, epoxy, gel-coat, polyester autobody filler putty (Bondo), and repeated layers of white glue or gesso are all common choices.
My favorite choice for this step tends to be a mixture of Bondo and polyester resin. By mixing them, you have complete control over the thickness. Making it thinner lets it be applied smoother, and have fewer pinhole flaws. Making it thicker allows you to fill in large defects and prevents it from dripping or running. The higher concentration of solids also makes it quicker to sand.
You can do the same thing by mixing together resin (polyester or epoxy) with some sort of thickening agent, such as colloidal silica (aka Cabosil). Bondo, after all is pretty much just a mixture of polyester resin and talcum powder. The problem is that dosing out the right amount of powder is sorta difficult, mixing the powder evenly into resin requires either a lot of calories, or a power drill with a mixing attachment, and you gotta wear a good dust mask or risk getting silicosis.