Here's what you can do on the cheap, get some zip-ties, a 15-25w soldering iron, 60/40 lead/tin solder, some heat shrink and a few simple hand tools like a knife, screw driver.
Anybody with a soldering iron and some solder would probably lend it to you, if not this would be the most expensive part at around $15-25.
If you are creative you may find some free or cheap sleeving material, as this would be the time to do it. Also it will help hide splices etc. Similar to what your PSU already has in spots. You will need larger heat-shrink for the sleeving, or just use electrical tape, I won't tell if you don't.
If you have everything pretty much where you want it, you can now start shortening the wires. Don't try and take apart the plugs, just cut it along the wire, preferably where the heat-shrink wont be seen if possible. Again, if you are putting on a sleeve, they will usually hide them half decent.
It's pretty straight forward, start of with simple circuits, like the fans, then progress to getting the bulk out of the PSU wires. Don't be scared to get rid of extra unused plugs etc.
Don't cut Sata cables or shielded audio cables (if you have them.) (Too much effort to splice nicely.)
Don't cut the motherboard cable(s), they should already be pretty good and is probably beyond what you would want to attempt this time around.
Obviously only trim whats need, sometimes you need the length to hide something.
If you don't want to drill (You may not have much room behind the MoBo tray anyways), your only other option is to fabricate a panel that runs top to bottom, between the back of the CD drive and the MoBo.
Thin aluminum or plastic can be cut with a good pair of scissors, or borrow a pair of tin snips from the guy with the soldering iron. If you are real ambitious, paint the inside of the case black to update it, or any other colour for that matter.
If you go this route you can always check back here for the specifics about soldering, it's pretty easy, the only real tricks are doing it neatly.
Getting rid of excess wiring and neatening what is there will be an improvement and your only practical option with your case.