The refer (fridge) is worth keeping, since a new one costs a lot, and for a few hundred, the 'innards' can be replaced, making the unit 'as new'. I think it's actually better though to sell or donate it. Most of them are pretty big!
The oven may have useful parts for someone else, but I would leave it with someone else to actually do that, unless you have unlimited storage space at home.
The furnace is definitely for the scrap heap. When they are old, the internal parts can rust out, making it unsafe. The only item I can think of that might be of interest to someone else is the fan.
Enjoy your new appliances!