Could be a severely corroded output jack - assuming that may be what it is, wrap some fine (800 or so) Emery paper (the black sandpaper) around a knitting needle, or a pencil or similar - stick it in the
jack socket and twirl it around for a while - that should dislodge enough corrosion to get you going (a spray with contact cleaner and mopping up the gunk with a paper towel afterwards is a good idea) - if it makes absolutely no difference, then you most likely have a broken lead somewhere - again start with the jack socket - if it has worked loose on it's retaining nut, it may have broken one of the wires running to it.
Good Luck - if your Strat is in fact thirty or so years old, bear in mind that it is getting well into the "vintage guitar" league, and if it hasn't been chopped and changed, it is actually worth a bit of money, so, if you can avoid the temptation, leave it as stock as you can!
Cheers,
David