Sounds like you have already had someone out to look at the situation. I am curious what they told you.
Regarding your original post, I can imagine using house jacks set on massive poured and reinforced footers dug into the basement floor supporting I-Beams being used to stabilize the house, and even allowing the old foundation to be repaired in segments. But I would not want to undertake it without a consultant or contractor on call. And of course permits.
I don't know about the conditions of your home purchase, but it appears you had an undisclosed structural defect that was passed down from two previous owners. Depending on law in your jurisdiction, you may have legal recourse that would help recover costs of repair. You should look into a consultation with a real estate attorney to determine if you have any rights. As a specialist, the attorney will also be aware of any grants the might be available for urban renovation projects, and how that fits your income and other qualifications.