How to determine IC function
You are on the right track.  You can usually determine which pins are input by measuring the voltage.  Do note that an output pin that is logic HI can have a voltage as low as 2.4V and still be within spec.

After you have identified which pins might be input, then use a 1K resistor to ground to determine which pins are inputs.  Touching a 1K resistor from ground to an input pin will result in the pin voltage dropping significantly, whereas an output pin won't drop significantly.  Mark all those input pins on your drawing.

Now use a 1K resistor tied to +5V and touch any pins that showing as 0V.  If the voltage rises slightly, this is an output pin that is LO.  If the voltage rises to 5V, this may be an open-collector pin that is HI.  Note that it might also be a "No Connect" pin.

Now that you have identified probable input and output pins, connect LEDs from the 5V rail through current limit resistors to all of the pins that might be outputs.  Then start applying stimulus to the input pins, first singly, then in combination.  Use a table to record any changes that you see.  The reason that you are driving your LEDs from 5V instead of Ground is so that you can see changes on pins that are open-collector.

Create a binary table with enough entries to cover all of your input pins so that you can be sure to test all possibilities.