I use Rubbermaid or similar brand storage containers of various sizes like those seen here:
This pic is from 2 years ago when I was still living in Palisades Park. I now have more than twice as many boxes of fodder (I have been collecting customizing fodder since the late 80's!). I organize them by putting like items together in the storage containers.
It's broken down loosley like this (I know there's more, but this is all I can remember off the top of my head since I'm not in my Hobby Room):
Starfighter shells (3 32 gallon tubs)
Starfighter parts (2 30 gallon tubs)
Airspeeder shells (2 32 gallon tubs)
Airspeeder parts (1 32 gallon tub)
Skiff/Sailbarge parts (1 32 gallon tub)
Non-repulsorlift Ground Vehicles (3 32 gallon tubs)
Non-repulsorlift Ground Vehicle parts (1 18 gallon tub)
Repulsorlift Ground Vehicles (2 45 gallon tubs)
Repulsorlift Ground Vehicle parts (1 32 gallon tub)
Diorama parts (4 55 gallon tubs and 1 39 gallon tub)
Freighter/Shuttle shells (2 55 gallon tubs)
Freighter/Shuttle parts (1 39 gallon tub)
Beasts Of Burden (2 39 gallon tubs)
Droids- whole (1 55 gallon tub)
Droids- parts (1 32 gallon tub)
Human figures- whole (1 45 gallon tub- soon to be 2 45 gallon tubs)
Human figures- parts (1 18 gallon tub)
Non-Human figures- whole (1 39 gallon tub)
Non-Human figures- parts (1 18 gallon tub)
Vehicle mounted weapons (2 18 gallon tubs)
Engines (1 18 gallon tub)
Cargo including crates, barrels and misc. (2 18 gallon tubs)
Mele Weapons (1 18 gallon tub)
Cloaks/Vests/Skirts/Capes (2 18 gallon tubs)
Armor/Belts/other items that go "on" figures (1 18 gallon tub)
Helmets (1 18 gallon tub)
Misc. "Mechanical" Parts/Greebles (1 55 gallon tub and 1 39 gallon tub)
Non-Weapon "Other" Accessories (1 18 gallon tub)
Backpacks (1 18 gallon tub)
All of these boxes are filled to the brim and I'm soon going to have to get more boxes as my fodder library increases.
All of my various Blaster pistols and rifles are sorted by weapon class and stored in the 2 60-drawer organizers seen here: