That looks like noodles having a bad day.
The only way you can clean up that mess is to disconnect a few wires, sort them out, and move on to the next batch.
In this case where you don't know which wire goes where, I suggest tagging each wire at both ends with a name and stuck with cello tape. So even if you have to remove all wires, you won't end up scratching your head as to what goes where.
Some of the wires look too short to be hidden and some are too haphazardly installed with wires hanging from one machine to another. You will need to come up with the best solution to the problem. Use those reusable plastic cable ties to tie together cables or use some casing and capping to conceal the cables.
Get a server rack if possible since this looks like some workplace. Keeping everything in same place, its easier for cable management.