I would purge toys as much as possible. Take note of what they play with regularly and what they dump regularly. Then sort into categories. Always find storage solutions after you've done the above and not in reverse order -- otherwise you simply end up organizing your clutter rather than ridding of it.
Are all three of your children the same gender? Because that would help tremendously in the purging of toys and design of your toy room. I would split the room up into five different categories (you choose them of course) - One category per corner and the 5th category in the middle of the room. Set it up the way you would a pre-school area - Plenty of space for multiple children to play in simultaneously.
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