RE: What types of glues to use to repair styrofoam?
Deep repairs with Elmers glue take forever to dry. The glue near the surface will dry first, sealing off the glue that is further down and prevent complete drying. The safest bet for a thorough cure is to use either epoxy or Gorilla glue.
If the foam is badly compressed, glue in a wedge of scrap foam [into the void] with Gorilla glue.