To answer the OP....
The only Omegas that are EOBD (EU's version of OBDII) are:
2.6 V6
3.2 V6
2.2 DTi*
2.2 petrol*
Thus older V6's do not work with generic readers, whatever the seller may claim about it working with post 1996 cars.
Officially, a 1996 Omega is a Tech1 or Tech1a car, and needs the Omega cartridge and the Omega multiplexor module (or a bit of resoldering).
However, the Tech2 is much more capable, and works on *all* Omegas with the exception of the following modules:
IR Locking
IR Immobiliser
U25DT engine ECU (the DDE 2.0 management system fitted to 1994/5 Omega TDs)
The Volvo will be EOBD, and thus work on any generic EOBD compliant reader that supports the correct protocols, which most new ones will. You will likely only get basic info (ie, P codes) from the engine management, and possibly drivetrain. Some, but not all, can read manufacturer specific codes (U codes), though cant decode them.
Manufacturer, dealer level, diag tools allow the full suite of diags, upgrades and reconfigurations that the dealer gets, though the tools are expensive, and usually require ongoing licencing. Even then, in some cases, some functions are locked out to all but franchised dealers.
3rd party tools aimed at specific manufacturers, such as the aforementioned iCarsoft, tend to be a significant step down from the dealer level stuff, and usually can only communicate with a small subset of the onboard systems.
The rather hopeless tool that cannot be mentioned is pretty rubbish when you buy the €600 original. The Chinese £20 ebay clones are a lot worse, and can be dangerous to the car - I used to make a tidy profit off collecting ECUs from the scrappy and reprogramming them for cars that said tool had destroyed. Whilst in general it seems OK for reading codes from most of the systems it can talk to on the Omega, I would be ultra cautious plugging it in to a Tech1 car.
*These seem to be strictly EOBD, and some OBDII readers struggle with them