You're right in thinking that at 18 months, dumping is practically an official sport. The rule for that is: dump one thing at a time! Then put it back, and you can dump something else.
And they're not quite old enough for disciplined putting-away, although you can begin teaching them by making a game of it.
All the same, I'd be inclined to organize some, as opposed to having one big toy box. My DIL has a plastic chest of drawers where the toys with little pieces live. My granddaughter (at 16 months) knows that's where these toys belong - and sometimes she gets them there. The pieces don't always get in the right drawers, but that's just a little mess to sort out later on when there's time.
You might think about taking stock of how many toys you have, and putting some away, assuming you have the storage space. If you could get out toys on a rotating system - say, rotate them once a week - theoretically your children could play with all of them, over time, and you'd have less clutter.
You're going to have some clutter no matter what you do. It comes with the territory. You'll do well to tame it to the point where it won't drive you so crazy. Continue to teach your children to love putting things back in "the places where they live."