As far as I'm aware, there is no way to construct a "true" heptagon using only a straightedge and a compass. However, there is an approximate way that might work.
To create a heptagon, first draw a circle. The larger the circle, the more accurate your heptagon will be. Then, using a dividers, set them to what looks to be the correct length of one of the sides. Walk the dividers around the circle until you have paced out all seven sides. Most likely you will land off the mark you started at, which means that your length needs adjusting. Adjust the dividers longer or shorter as necessary, and repeat the process until you have the circle divided into seven even segments.
Then, draw seven lines radiating from the center of the circle to each of the endpoints you stepped out with the dividers. These will divide your circle into seven even slices.
I imagine that you will want to start out with a long, straight-grained dowel of a diameter that suits your size. Place this dowel on the circle you just drew, making sure that the dowel is centered on the circle. You might want to make some sort of clamping jig for this operation. With the dowel coincident with the center of the circle, mark a line for each of the seven pie pieces you previously drew.
You will now have seven marks on the end of the dowel spaced evenly. Next, carry these lines along the entire length of the dowel, making sure they are exactly parallel with one another. At this point, you will have seven parallel lines along the length of the dowel that split it into seven even segments.
Now, take the dowel and place one end against a planing stop (or lightly pinch it between two dogs with your workbench tail vise, see image below). One of the segments you marked should be facing directly upwards. Using a hand plane (preferably a jointer plane), begin planing away the facet. Stop when you get down to your lines. Repeat for each of the seven sides of the heptagon, and you will be left with a heptagonal dowel.
(source: Popular Woodworking)
At this point you can cut the dowel into slices to produce your corner pieces for your shapes.
For drilling, make a jig that cradles the slices such that the top face is horizontal (perpendicular to your drill press). Then it's a simple matter of drilling out for the rods with the drill bit you want and at a depth that works for you.
Of course, if you don't want to go to the trouble of making a heptagonal dowel (it's a lot of fiddly work), you could just use a regular dowel, slice it up, and mark your seven segments on the end of the slice. Then, make a drilling jig that holds the dowels, and that has a mark directly on the bottom of the area that holds the dowels. Then, all you have to do in index your marks to the bottom of the jig and drill your holes, rotating the dowel slice each time.