Can anyone suggest a solution in which to clean my gears, forks and drum? There was an incident that caused some metal shavings to be in my engine for a while and I'd like to be sure they're all cleaned before put the engine back together. What's everyone think? Dish soap? Kerosene? Mineral spirits? Something else?? See below for a pic of the gears and thanks!

I guess Kero then wash it off with garden hose & oil it up. I just used to use petrol in the old days. If you cant see the shavings then they can't be there. It'll be good.

Brake clean. or Kleen as they call it

I am a huge fan of  BBQ lighter fluid, Walmart is 40% cheaper than anywhere else 

Gosh that sounds pretty volatile. mind you i'm thinking of totally bathing it in the stuff, kerosene whatever, like about 10 litres of it & roll the shafts around.

Definitely kerosene, years ago we would have it in the parts cleaner until more modern, environmentally better fluids came but they never cleaned as good. Then let dry a while then use an air line to blow dry and clean , followed by oiling. 
I recently purchased a new engine case oil plug that's magnetic, properly a good idea too.

I use mineral spirits, (it is low volatility, relatively cheap, and does a good job of disolving oil & grease) then blow dry and follow up with detergent/hot water and another blow dry.
alnarv

Autozone degreaser, then blow dry. It's cheap, I keep a supply.