How was large shipping (boat) freight handled before modular shipping containers?

Was it all just wooden boxes and cargo nets?

Pretty much, along with sacks, metal boxes, barrels and anything reasonably durable you could cram stuff into and handle relatively easily. I believe the technical term is
Break Bulk.

Also the cargo would be manhandled on and off the ship by dockers, which resulted in an interesting rate of breakage and shrinkage (theft).

Containerization reduced both - and reduced vulnerability to strikes

How To Tell When You’re Tired is an excellent read, and you’ll get a good sense of what a longshoreman does.

Factoid:

That’s well over a 6000 times improvement in efficiency.

Made for a lot fewer drunk sailors, though. We Navy types had to take up the slack from the merchantmen.

Is 'break bulk" still the term used for cargo carried by aircraft?

Remember all those sleazy waterfront bars from the movies? They don’t exist anymore, because instead of 100 longshoremen manhandling cargo out of the ship’s hold, you’ve got 1 guy operating a crane. The bars and whores loansharks and other businesses that catered to the longshoremen went out of business.

“Stevedores” is what I always heard those guys (Longshoremen) called.