Lay the butcher block on your work surface, finished side facing down. Cut the four cedar 4-by-4 posts to a length of 29 inches. Set them in place in the four corners of the cart top but do not secure them.
Cut the 2-by-2 cedar boards so that you have two that are 22 inches, and two that are 16 inches long. Screw the pieces as support bars between the legs at a measurement of 15 inches centered from the top of the post and centered on the post width. Do this by screwing in a long side support first. Set the support between the two posts. You can strap the posts together with a strap clamp if you have trouble holding the support in place while you screw in first one end to a post, then the other. Use a counter sink drill bit to set the screws down 1/4 inch into the wood so the table will have a finished look when complete.
Screw the four casters in place on the bottom of the legs.
Turn the table upright, and screw the butcher block top down to the legs, again countersinking the screws to set them down into the wood.
Screw a 26 inch piece of 2-by-2 cedar across the center of the middle shelf, lengthwise. This will provide a center support for the slats. Screw it to the 16 inch end support pieces so the top is level with the others. Counter sink your screws.
Cut three of the 8-foot 2-by2 cedar boards into 1-inch slats by cutting them in half lengthwise, called ripping, with the saw. Then cut them down into smaller slats for the middle shelf of the table. You will want 11 pieces that are 24 inches long, and four pieces that are 16 inches long. Cut a 1-inch wide block of wood to use as a guide to place your slats.
Install the slats for the center shelf by starting at one end and screwing a 16-inch slat on top of the end support between the legs. You will add a slat every other inch across the shelf: the slats will be screwed on the supports widthwise, front to back. Set the 1-inch block jig next to the support, then add a slat next to it. This gives you a quick way to measure an inch between slats and set them in place. Screw the second 16-inch slat in place, then begin adding the wider slats across the middle using the same technique. Finish off with the two shorter slat pieces at the end, between the legs.
Place a bead of wood glue on each of the wood dowel plugs and set them into the screw holes where you counter sunk all your screws. Tap them lightly with a hammer with a rag over the top of the head to avoid denting the dowel pegs, until they are flush with the wood.
Sand the entire cart until smooth, and seal the wood with the oil by rubbing on a tung coat with the clean rag.