Should I install a vapor barrier on the bottom of my garage ceiling?
Yep, the 120 year old houses do make life more interesting (and expensive and/or colder.)

Use an air barrier that is NOT a vapor barrier. More commonly known as housewrap. Vapor moves through, but bulk air movement is reduced.

For insulating inside the floor joists, either blown-in cellulose (which supposedly has very little issue with vapor, due to having very little air movement through it) or a sprayed foam product. Getting good fill blind (without blowing out the ceiling, in the case of the spray foam) is tricky.

I presume you don't want to rip out the ceiling for better access - but you really need to think hard about getting some drywall below the XPS (or XPS and added air barrier), or you have (and have now) a major fire hazard - plastic materials exposed in a garage that's below occupied space. The plaster ceiling above it may not burn through for a good long time, but the smoke from it will do you in even if the structure is unaffected by by a fire.