ZAU Controller reported similar sounding airspace fixes - SUPER and SOUPR.

Narrative

I was working the 3 SE area lows all combined because the traffic volume at the time permitted it. There was a line of ORD arrivals that I was sequencing and not much else going on so I had started a relief briefing to another controller. During the briefing; there were at least 3 departures off of the ZZZ airport; 2 of which were military aircraft.The HILLTOP MOA; military airspace in our area was scheduled to go active around this time; but neither of the two military departures were routed towards our scheduled airspace. Aircraft X; a military flight of 2; was the first military departure that was on a northeast bound heading in the climb and I climbed them to their requested altitude of FL230 on check in because I did not have any traffic in their way. Their route was ZZZ..SUPER..ZZZ. The 'SUPER' waypoint in our database was showing a direct line to the west.About a minute later; Aircraft Y also takes off on a northeast heading; but their route is ZZZ..BAX..ZZZ; and BAX is to the northeast. After seeing Aircraft X still on their northeast heading; I'm assumed they were assigned a heading with ZZZ approach and did not tell me about it. However; they were actually traversing towards the 'SOUPR' fix; which is to the northeast. I recleared Aircraft X direct SUPER because it looked like they were going the wrong direction and continued with the relief briefing.After seeing that clearing Aircraft X direct SUPER did not change their heading; I inquired on how to spell the waypoint they were direct to. To which they told me the correct fix. The controller I was giving the briefing to was quick to get on the D-side to help with coordination while I continued to do the other control instructions throughout the other parts of my airspace.The aircraft were traveling so fast over the ground that I did not have enough time to coordinate with the C15 and sector 81 in time before getting into their airspace with both military planes.Recommendation: ZZZ approach should be careful with the spellings of their routes. In addition; the three immediate departures off the same airport added more workload than I was able to accomplish in the short amount of time when military aircraft are going northeast bound out of the OLK sector.Splitting of the OLK sector only would have helped with the situations; but I believe that if it was BEARZ/OLK (the configuration we normally run); the situation would have been the same and there would not have been enough time to coordinate the necessary information and fix the inappropriate route.There also was not enough staffing to support the split of the low sector at that time because overall; the traffic count was light and not difficult. The biggest complexity factor was the wrong route; speed of the planes; and short proximity to entering other controllers airspace. Doing a relief briefing during the situations also took our focus away from the potential situation; but it helped having another person get the coordination done while other things were happening in the sector.