Bonding polystyrene foam to steel and wood is an application that was traditionally done with contact cements or other solvent-based adhesives. Due to health and flammability concerns, however, the modern trend is to use 100% reactive systems.
I would suggest using a reactive hot-melt urethane. These adhesives are used routinely for this type of application (e.g., in the manufacture of insulated garage doors or in the construction of panels for recreational vehicles). Hot-melt urethanes can be applied as beads, sprayed, or roll coated.
The hot melt will give you rapid fixturing, with a short time to handle the parts; the adhesive will then crosslink due to reaction with atmospheric moisture. Full strength should be reached within 24 hrs. Keep in mind that application equipment tends to be rather expensive if you need automatic assembly.