Pull up/ Pull down resistor

As per the schematic provided, if all 3 inputs were sharing a resistor, then any of the lines being pulled high via the switch would raise all 3 lines to high, countering the purpose of the design - the MCU would not know which switch position is selected.

A common way of reducing part count, not resistor count, for such designs is to use a common bus resistor network or array:
(from here)

These are available as through-hole SIP/DIP as well as SMD, in a variety of resistor counts, depending on your needs. The bus pin is connected to ground, and the other pins are connected to the respective MCU inputs as in your schematic. (from here)

(from here)

Strong means low resistance. Weak means high resistance. Of course low and high are relative terms, and so are strong and weak. The reference for this relationship must be inferred from context.

A strong or low resistance pull-up/down resistor is good because the time constant formed the load capacitance (often, the input gate capacitance, and the PCB trace capacitance) is small, so rise/fall times will be short.

A strong pull-up/down resistor is good because noise currents from unintended coupling and EMI will result in smaller noise voltages. (Think about Ohm's law)

A weak or high resistance pull-up/down resistor is good because it will not require much current from the driving circuitry to work against the resistor. Batteries will thus last longer, parts can be smaller and don't get as hot.

Of course, you usually want all of these things, but a resistor can't be both. A discussion about strong vs. weak is usually clarifying which of these concerns (or perhaps others) are more important for a particular application.