Note that any keyboard adapter will allow "users" to interfere with each other's "keystrokes".
Each axis of a digital joystick has three permitted states, usually requiring two bits. Each button is another bit. Therefore, four single-axis joysticks with one button each require 12 independent bits (since they can all be operated asynchronously).
An analog joystick joystick input can only be read reliably to within 1% or so--allowing a maximum of 6 independent bits to be read. (And, since any switch can be operated at any time, a sample-and-hold would be needed to guarantee no false reads as a result of a switch changing state in the middle of a read.)
So analog sensing is out unless the inputs won't change during the read, and can reliably provide only about 6 independent bits of input per read.
If you really need a lot of parallel inputs, use a general-purpose parallel port card with an external joystick adapter.