As far as I am aware, the technical differences are somewhere between small and non-existant.
The real deciders are going to be the electrical circuits for on-train facilities. Provided that all systems run at the same voltages and on the same circuits there should be no reason why they can't be interchanged. However, there may be some differences between AC units and DC units as a result of the different power supplies. Also, an AC unit requires through-wiring for certain control functions that a DC unit doesn't require (e.g. raising and lowering the pantograph). If there is no wiring to support this function on a DC unit vehicle it can't just be used as a straight swap into an AC unit.
The control circuits themselves appear to be fairly standard. For example, Cl317's, Cl321's and Cl322's can all work in multiple with each other without any restrictions. I believe that you could add Cl319's to that list because they have been used to provide the power for Cl317 "drags" onto the 3rd rail network, although I'm not sure they've ever worked in multiple in passenger service or whether there are any restrictions that would prevent them from doing so.
However, I don't believe that it's quite so straightforward when it comes to swapping vehicles between 100mph OLE units and 75mph CRE units (e.g. Cl455's). Quite apart from the potential for differences within the wiring loom, a DC unit lacks the additional yaw dampers on the bogies that it's AC counterpart has as standard. Without these it can't run at more than 75mph.
As for some of the specifics of your question:
Cl319's do not have additional controls that allow them to be dual voltage. The driver selects the power supply simply by raising or lowering the pantograph. If the pan is down and the shoes are on the 3rd rail, the unit will draw power from that. However, a Cl319 does need to carry additional wiring compared to, say, a Cl321 in order to connect the shoes at each end to the motor coach in the middle.
For the same reason, a Cl321 DTOS could not be formed up with a Cl456 DMSO because it lacks shoegear. This means that the unit would only have one pair of shoes at one end of the unit only, which is clearly not a good situation to be in. I guess it might work with a Cl319 DTOS, but I am not entirely sure that the control circuits would be entirely compatible. A Cl319 is an AC unit that happens to be able to work off the 3rd rail too while the Cl456 is a pure 3rd rail unit designed to be compatible with Cl455's.
The Cl508 TSO's in Cl455/7's is possible because both classes are pure 3rd rail units and because the TSO has no major systems that are not standardised across the entire EMU fleet. I'm not sure that they were just "slotted in" without any modification whatsoever, but they really only required some juice for lighting and heating, etc, and 7 bar main res pressure for the brakes and the doors. As hinted above, provided that all the systems on the Cl508 TSO were on the same wires as on the Cl455 and run at the same voltage (or were modified to ensure they were), they should be fine.
O L Leigh