The shifter knobs are interchangeable.
Actually, the answer is, unfortunately, not that many. Most of the body parts will be interchangeable, but not a ton else. The LXi has larger front brakes, different shocks or springs, if not both shocks and springs. The engine is different, obviously, as one is fuel injected and the other is carbureted. IIRC, the FI engine has a higher compression ratio. The front sway bar is thicker on the LXi (I think), and there is small one in the rear, where none exists on the DX. The LXi has 14 inch wheels, the DX has 13's.
The transmission is probably interchangeable, but I'm not certain, because they might have different final drive ratios. If you're going to get the transmission, you might as well take the drive shafts, and the front suspension stuff, in case you need them.
From your old car, I would get the side glass, the combination switch (headlights, turn signals, wipers) from the steering column, and the relays that control the pop-up headlights.