I think you have to decide what your plan is. Is he now living with you? Just visiting, staying there while mom and dad go somewhere like a long weekend trip? Are you babysitting him while his parents work now?
Once you define your role in it all you can decide which way to go.
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If I was babysitting my 2 year old grandson and he was going to be at my house 5 full days per week until he starts school I'd clean my house and put things up he isn't supposed to have contact with.
Remember that anything that can fit through a toilet paper roll center is a choke hazard for this age child. A toy that has small wheels like Hot Wheels are choke hazards, puzzle pieces, raisins, marshmallows, gummies, Legos, and more.
A 2 year old can drown in the toilet too so keep the bathroom doors locked/secured with devices you can get at hardware stores and even Walmart. Cleaners and laundry stuff goes up over the washer and dryer now, over the sink, out of sight and out of reach. Period. They drink they die. They put their hands in Drano they lose their hands. Etc....
Then work on teaching him what he can and cannot touch and what boundaries you have. A gate in each doorway where he can't go is a lifesaver. Putting stuff up out of his reach is wonderful for him and you.
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If I was taking in one of my grand kids and they were 2 I'd set their room up and teach them that toys that come out of their room go in time out. I do not allow toys all over the house. Their toys are theirs and they need to keep them out of the general space everyone uses.
I would give them plenty of age appropriate toys BUT I'd put some up so we could rotate the toys every couple of months. This way it's like having new toys to play with. I'd also make sure that there weren't a LOT of toys on the shelves or in the toy box because when they see chaos they feel chaos and they don't deal with it well and won't play with toys at all.
So put out about 12 toys and put the rest up and keep them fresh by changing them out. Teaching him the rules at your house should be done with a lot of patience if he's living there now. He's probably going through a lot of fear and missing his parents.
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If he's just there on vacation and mom and dad are there you need to have a talk with them. Ask them how to proceed and keep him out of stuff without you having to move every single thing in your house that is in his reach. They should be watching him too.
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If he is just over he needs to learn to mind you. It's your home and he's not supposed to act like this.