I'm from the west coast as well (born and raised in WA, currently live in Utah). Maybe it's regional? If someone said "box of strawberries," my thoughts go to those "you pick" places where you fill up an open-top cardboard box of strawberries, or those fruit stands that sell those same cardboard boxes of strawberries. I've never called the plastic clamshell containers a "box" though.

But yeah, I'd probably understand you given context, but it's not how I'd refer to them.

Words can be pretty regional, so maybe it's a Cali thing. Idk, my family in Cali are immigrants who speak a different language, so I don't think I've ever heard to them refer to the container of strawberries in English.