Can the Prius wagon hold 4 foot x 8 foot pieces of plywood, or if not, tow a trailer that can?

The OP said: "As far as material delivery, I don't think so." Where do live that lumber yard deliver for free?

If the land is rural, it's often not practical to have large loads of unused lumber sitting on site unless someone is always there to guard it. Even when a house is going up, thieves will come in and rip out stuff. After I had a house built in a rural area 40 years ago, I tried to help others by driving away material thieves from nearby houses that were under construction. Usually it was enough to just drive up to the thieves parked vehicles and make sure they saw me taking photos of their license plates before I drove away. I tried not to confront them - too dangerous - and sometimes it was in the middle of night. It was sad - especially when I saw guys with their children with them stealing stuff.

 

1/2 ton PU.

 

It recently took me three trips to get the complete wet/dry vacuum, hoses and nozzles over to our daughter's.

 

boston. very competitive. if youre building a house, it's all free, even small emergency deliveries.

 

Not in a Prius; it's the two electric motors and some gears. No belt.

 

I've hauled a lot of plywood with my Prius V. On the roof. I have a roof rack for kayaks. It's not flat, I've got fittings to cradle the kayak so the plywood is uneven, no problem. I've also hauled lumber and stuff for years on a variety of vehicles.
A rack is okay, but not necessary. A moving blanket to protect your paint is more than enough.
The biggest issue is tying down the load--and this is the most serious issue.
For my kayaks and for hauling plywood and lumber the most important tie downs are the front and rear. Plywood or any sheet goods will catch the wind and try to lift off. This is a powerful force.
All Prius's have no good tie points in the front of the car. To get around this, open the hood. You'll noticed two fender bolts on each side. Remove the front one. Get some webbing, 3/4 or 1" thin is good (I use old roof tie down webbing) about 12" will do, double it and on the open end use a soldering iron or a hot nail in pliers to burn holes for the fender screw. You don't need new or longer screws. When you screw the loops in you can have them stick out the sides of the hood, or you can tuck them underneath. These make reliable strong tie points.
I usually tie an arc across the two hood loops and then run two ropes towards the back to keep the front of the plywood down. At the back there's one tie underneath. Good enough. Across the two rear doors, windows open I tie a rope around. I put the rope through the open windows instead of closing the door on the line. When you jam it in the door frame you can cut into the rubber seal.
If you have any doubts after you start driving, pull over and check everything. It's easy for knots and rope to slip.
For lumber I usually tilt back the front seat, remove the head rest, back seat down of course. Make sure if it shifts it doesn't cause an accident or go through the windscreen. If you go for a roof rack, those cheap ones with the board and rubber suction cups, if properly attached are as good as any $400 Thule/Yakima rack. Hope this helps. If this sounds good but my description is not understandable, let me know and I'll post some photos.

 

I've hauled plywood sheets cut down to 2 x 8 in the Prius cabin. Very awkward tho, and not recommended if you are doing it on a regular basis. Using a roof carrier, as SBCA_CA describes, is the way to go. Wish I had thought of that at the time.

 

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The Torklift 2” hidden hitch and the Detail K2 utility trailer and you are set! That’s my set up.

Take it slow and safe with larger loads and you’ll be fine.

 

I know this isn't the same, but I have fit 40" wide planks in my Gen 2.