Blue jays are varmints.
Virtually all of the feeders with which I have hunted use corn.
My experience with feeders has varied. Some people believe that with feeders, all deer, including trophys, simply walk under the feeders and wait for you to shoot them. While this can be true to some degree, in my experience is accounts for less than 50% of the truth.
I say this because, at least to me, feeders are used to attract deer to an AREA, not just necessarily under the feeder itself. This is especially important during the rut because the does go to the feeders and the bucks follow the does. Granted, bucks can, and often do, eat along with the does under the feeder, but during the rut the bucks are more interested in mating than eating. Under these circumstances, they usually hang out around the area and wait for the does to come back. It is at this point that I too like to rattle the bucks out of their hotspots where they are waiting for the does.
More importantly, there are often times of drought when the deer simply have no available food sources. As such, feeders are usually the only source they have. In fact, you can usually see them so thin and unhealthy that it looks like their rib cages are about to stick out.
During these times, the bucks will come in under the feeders, but I shoot does so that, as part of management, as there are less animals to feed, the ones left over will have more food to eat, and thus become healthier.