I think you need to get a structural engineer out there ASAP to investigate; I would be worried too!
Your city's by-law office might be able to refer you to someone who can help.
It might also be worth getting in contact with your insurance company - they might have their own engineer come out.
If you think it's really about to fall over you might opt to call the gas company to come shutoff the gas - the last thing you need is a fire added to this.
You need to make a judgment call on whether to stay in the house while you determine what's going on. Being dislocated at a hotel is not fun, but if your life is in danger, its a small price to pay. If you do leave, turn off the water and electricity too.
Good luck!
You can do it. Certainly.
There was a recent episode on this for "this old house". They basically suggested cleaning out the loose fill and then replacing the old mortar with fresh mortar. It looked tedious more than anything else - but doable by a homeowner. I've re-mortared and chinked stone foundations. It's a surprisingly high maintenance experience compared to poured walls.
The good news about stone foundations is that with proper bracing, you can fix up almost anything well enough to sell it to someone else who enjoys huffing dust, cobwebs, squirrel mummies and Radon Gas. But for the most part, it's like fight club - we just don't talk about it.
With improper bracing, you can experience the joy of being crushed to death, or lose an eye due to the magic of newtonian physics while you learn about shear loads and amateur metallurgy using those hydraulic jacks you bought at Harbour Freight. It's very educational.
A well built stone wall can always be repaired with less trouble than concrete foundations. The mortar and chinking is mostly for aesthetics, anyway.
Sealing the walls is fine, as long as you do it on the outside first, and then and only then do the inside. You'll have to dig down to the foundation to do this, and that bracing is an issue on the outside as well.
Now the part you won't like. I did this in high school for a relative who had a nearly 200 year old house with a sandstone & rock foundation, in a damp (flood plain) area. It looked great, but ultimately it was wasted effort. Exposed rock and mortar foundations will always breath, sweat and disappoint anyone expecting a modern basement experience. You can apply gallons of sealer, but it will simply create areas where it perforates.
These foundations were designed to keep out animals, hold up your house so it doesn't rot all that quickly and very little else.
They will always be home to spiders. You can seal it with gunnite or epoxy and it will still allow infiltration. It might look OK, in that "I love Halloween" fashion so popular with the gothic/serial killer/lonely artist set, but it will never be a comfortable space.
You might build a second wall that can be plumbed, framed and sheet rocked, but it won't solve much over the long run, even with substantial vapor barriers and ducting. The walls will still slowly shift, moisture will come and go, and you'll never be happy with the low ceilings.
So in summary: You can redo the walls. You can seal them. You can even box them in and add ducting, insulation, AC and lighting. It's still going to be a basement that weeps moisture due to temp and pressure differentials.
Best Answer
The safer and more predictable method (probably also cheaper) is to jack the house and build up, not messing with the footings. If the lower foundation is in good shape this can be a relatively simple approach if you work in concrete masonry unit lifts (i.e. an evenly divisible by 8 inches lift for most concrete blocks - perhaps 3 blocks or 2 feet for yours.) You raise the house somewhat more (well, unless you are nuts, your professional house movers do) and build the new block wall (reinforcing probably a good idea to ask your engineer about) on top of the old wall, then set the house back down on it.
Another fairly common option with more dire foundation issues is to either build a whole new foundation and roll the house onto it, or roll the house off to the side and build a new foundation in place, then roll the house back onto it. This requires space to do that, but it is considerably cheaper to move the house than to build the foundation while the house is in the way. However, the latter approach is also seen.