Why can Ohm's law be used in a linear circuit with multiple equivalent resistors without being given current?
As Dmitry noted, there will be a current flowing, but its actual value is not important, as it disappears when you calculate the voltages.

Take 4 resistors in series, each of resistance R. The total resistance is 4*R, and the current is 1/4*R. The voltage across any one of the resistors is U = R.I = R * (1/4*R) = 1/4V. That last expression doesn't contain I (=1/4*R). (And, maybe more important, neither does it contain R.)