After reading all posts, I'm pretty sure I follow the problem here. This is what I'm hearing:
Up each side & top of the old window jamb there is (was) an innner strip of wood (the inner sash stop), a center piece (sash guide), and an outer board (outer sash stop). You've removed the inner stop and the guide strip. The original jamb is out of square enough that the open distance between the L & R outer sash stops at the bottom of the jamb is almost equal to the outside width of the replacement window's jamb, so the bottom & lower sides of the new jamb are able to nearly "escape" outwards....right?
If the replacement window fits better (tighter) through the rest of the opening, this is pretty common & you can caulk that joint to get a seal.
If the fit is pretty loose all the way up, I'd add an additional trimmer, maybe like the inner sash stop (½" X 1½") to give you a better coverage. Normally the replacement window's outer stop flange will be about 1" wide, so you should have room to add some material to each side of the original jambs if need be.
As far as the storm windows, you can leave them on, but be aware that if you do you'll likely have to remove them from the outside if you ever want to take out a glass panel or screen frame for repair or cleaning. Once the new window jamb is in place you normally cannot tilt the storm sashes in far enough to remove them from inside the home.
Hope that clarifies things for you Jeremy; I'll keep an eye out for further questions. Good luck