ZID Controller experienced operational error at FL320 involving three aircraft that resulted from an incorrect altitude clearance readback that was missed.

Narrative

Aircraft #1; Aircraft X; northbound level flight at FL330 on the WEEDA1 Arrival. Aircraft #2; Aircraft Y; westbound level at FL320 direct MIE. Aircraft #3; Aircraft Z; northbound level flight at FL330 on the GEMNI2 Arrival. Aircraft Z and Aircraft Y were traffic. Aircraft Z was issued clearance when clear of Aircraft Y to descend from FL330 to FL300 at 1;500 FPM rate of descent. Aircraft X mistakenly took the clearance for Aircraft Z. Aircraft X read back clearance stating the altitude to maintain; then the rate of descent assignment; then the aircraft call sign. I missed the incorrect call sign readback. Aircraft X initiated descent with traffic Aircraft Y at FL320. I noticed Aircraft X descending and issued clearance to climb to FL330 and fly heading 270 degrees and issued clearance for Aircraft Y to fly heading 360 degrees. Aircraft X took the clearance for Aircraft Z; and when Aircraft X read back the clearance using a 'nonstandard' radio format instead of responding with the call sign first; then the control instructions; I failed to realize the mistake.