I have an older house with some outlet plugs that don't have the ground third prong. Some have the older 2-prongs. I'm in the process of changing all plugs and switches to the decor style. I want to replace this 2-prong outlet with a 3-prong outlet but when I test it its an open ground. Without having to run a ground wire to this plug, is there any other way to properly ground this outlet? Any ideas?
No the receptacle (plug; outlet) cannot be grounded without running a ground wire.
But there are other things you can do to make it safer, for example put a ground fault circuit interrupter on that circuit.
Older conduit and BX cable installations that may have had the metal sheathing forming a ground path may or may not still have a reliable ground path due to oxidation, loosening of screws and clamps, etc.
If you want to put a three prong receptacle there and not string a ground wire then you must put in GFCI protection and also label each affected receptacle with "No equipment ground, GFCI protected." One GFCI unit whether in a receptacle unit or in a breaker unit can protect several receptacles downstream or even the entire branch circuit.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.