Once you have all the clamps on, take off the scraps of hardboard. You can clean up the glue squeezeout with a damp rag.. When the glue is dry, trim down the strip flush with the panel using a router and a flush-trim bit. Then cut off the ends of the strip with a flush-cut saw, and clean up with a block plane, an edge scraper, or a sanding block. Leaving the ends in place while you route the edge helps support the router.
The decision to be made with respect to the end vise is whether the support plate should be mounted to on the inside or on the outside of the stretcher. Mounting the plate on the inside of the stretcher reduces the reach of the vise - it can't open as far, because the support plate is back from the edge by a couple of inches. But mounting the plate on the outside of the stretcher means that we need to add some support structure for the inner jaw of the vise, which the legs would have provided if we'd mounted the plate on the inside.
Applying the oil is easy. Put on some vinyl gloves, pour some oil in a bowl, take a piece of clean cotton cloth the size of washcloth or smaller, dip it in the oil, and apply it to the wood. You want the wood to be wet., you're not trying to rub it in until it's dry. Apply oil to the entire surface, and then go over it looking for dry spots, applying more oil as needed. After fifteen minutes of keeping it wet, let it sit for another fifteen minutes. Then apply another coat of oil, and let it sit for another fifteen minutes.