My first guess is differential, because...
1. Wagon - easiest vehicle for diff noise to be heard in and it can echo around to the point where you can't tell where it's coming from.
2. Whining hum - yep that's the sound diff gears make when they or the bearings are worn.
3. Happens most at low speed when cold - diff warms up, the oil warms up, plus the gaps reduce and oil gets in the gaps.
4. And when coasting - ooh diff backlash!
5. 260,000kms - gears wear and so do shafts and bearings. Drain the diff oil, run a magnet through the oil you drain out of it and see what it picks up.
If the oil is clean the seller may have already done the recommended and replaced the diff oil with a slightly heavier grade and a additve. If it is grey and/or sludgy I would put any cheap normal diff oil in and drive it for at least 30 minutes to 1 hour at highway speed to warm it and drain again then put in a good diff oil suitable for that model and its high mileage, perhaps with an additive.
ASSUMING you have a non-LSD V6:
I think GM recommend an 80W-90 mineral oil be used for your model
Gear Oil 80W-90 is a premium mineral automotive gear oil manufactured with modern extreme pressure additives and friction modifiers, meeting the requirements of API GL-5/6 and MT-1, as well as many other manufacturer specifications. It contains the correct dosage of limslip additive eliminating...
www.penriteoil.com.au
SHIFT EZE is a transmission and gear oil additive formulated with PTFE (Teflon) and molybdenum to improve shift quality of manual transmissions and quieten noisy drivetrain gear systems such as transfer cases and differentials. It improves cold changing performance and provides increased load...
www.penriteoil.com.au
I would warn against jumping straight up to higher viscosity 80W-140 synthetic oils for Limited Slip Differentials if your wagon doesn't have one.