A 3 wire dryer circuit is X-Y-N (usually red and black, and always accompanied by white).
Optional grounding may be accomplished by daisy chaining a separate ground wire from the dryer frame to a known ground.
A 4 wire (including ground) dryer plug may not be connected to a 3 wire circuit (without ground).
The average homeowner who lost his house in the Oklahoma tornadoes should move for good and not rebuild. Too much complexity watchdogging the contractor. Too much a chance to be defrauded.