Cleaning masses of pieces

Are there any easy tips on how to clean off the cutting oil without having to wipe each of 168 pieces individually?

There are a variety of approaches. Some put multiples into a basin of water as they are cut.  Some with soap added, some with window cleaner or vinegar.  When all are cut, the pieces are swirled around in the water/additives solution and laid out on kitchen towels to drain while each is polished with clean towels.  Some put the glass in a bag into the dish washer.  This leaves the glass with the residue of a number of corrosive chemicals on the surface.

If you must put additives into the soaking water, I suggest you use a combination of 1 part water, 1 part isopropyl alcohol, and 1 part 5% citric acid.  Avoid the use of vinegar. There is a significant risk of etching the glass, leaving a dull surface. Citric acid will not affect the glass, nor leave residues after rinsing.  The alcohol will speed the drying.  But see this post on another better chemical than Citric acid. You can leave glass soaking in tri-sodium citrate for up to 48 hours without etching.

Essentially these practices are to soak the pieces until all are cut to have a mass cleaning and drying session.

But I don’t use oil in my cutter and so I can follow this procedure:

clean the glass sheet first,

score with no oil in the cutter,

break,

set aside to assemble.

Prior to assembly I clean each piece with isopropyl alcohol and a polish with paper towel.

Cleaning glass for fusing is much simpler if you do not use oil in the cutter.  There is no absolute necessity to do so.  The glass will score and break very well without oil.