My understanding is that the 3rd terminal, the one that the drill doesn't use (or at least my drill doesn't use) is connected to the negative terminal of the battery via a thermistor and is used by the charger to regulate the temperature of the battery while charging. Important for Li-ion cells.
If that is the case then a "proper" battery will show about 11V between the +ve terminal and each of the others, while they will have nothing across them. A resistance measurement between these last 2 will show the resistance of the thermistor - a few 10s of ohms perhaps.
You imply that you don't have the charger that goes with the drill, so presumably you made up your battery from robust, non-exploding cells like Nicads and charged it in some sensible way.
I can't see why that shouldn't work.
On the other hand if you did try to charge it on the dedicated charger without presenting the 3rd terminal I can't imagine the charger working.
In my experience measuring the open-circuit voltage doesn't give a give a good indication of the state of charge or the health of a battery, unless it's absolutely flat or knackered.
Can you monitor the battery voltage while the trigger is squeezed?