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.