Why does my BA Ford Falcon overheat while under load or driving up a hill?

The reason the car overheats under load or when travelling uphill is simply because it's defying gravity and, therefore, doing more work in those circumstances. Think of it as a person using a staircase. They'll go down the stairs easily, but they'll sweat more going up them, and more again going up the stairs with a suitcase under each arm. In a car's engine, hauling a load or driving uphill requires more throttle which, in turn, injects more fuel into the cylinders. And more fuel burned equals more heat. It's as simple as that.

If you've replaced the radiator, water pump and thermostat, you've started logically enough, but simply replacing bits and pieces is not the way to proceed as you've already discovered by replacing parts that were probably good (and didn't fix the problem). You could have a collapsed radiator hose (Were these replaced, too?) or a problem with the fuel-air ratio which can make a car run hot when it's under duress. The steering column sounds unrelated, but if the wiring to the dashboard was damaged during this process, it's possible that the temperature gauge is reading incorrectly and the engine may not be running hot at all. An electronic scan will be able to check the actual running temperature as well as uncovering any fault codes the computer has logged.

Don't rule out things like a build up of debris inside the cooling passages in the engine that could be blocking the flow of coolant. And a check of the radiator overflow bottle is a good idea. These have been known to perish and crack on Falcons, allowing some coolant to escape, leaving you with a low radiator level when you need it most.