Valerie, If Jennifer & I have understood this right, you are saying there is no sill plate; between the studs you could see open wall cavity that extends both above & below the floor level, and the floor does not extend out under or between the studs?
Valerie, if that is the case, your home was "baloon framed." What's done most commonly today is called "western framing." In baloon framing, the framing looked like a series of "templates" that formed the entire outer shape of the home, and the floor joists were then side nailed to the studs, instead of building walls which sat on top of a framed & decked floor.
This type of construction can be hard to seal off, because the stud spaces are wide open to both the attic and the basement/crawlspace below.
The backer rod sounds like a good start, but you may also want to check into stuffing some insulation into the top & bottom of each cavity if you find that this is the situation; this will dramatically cut the draft in the walls. Best of luck!