This Wheat looks like it's struck off-center on the obverse, but the reverse looks fine. What's the proper name for this? Is it just an off-center strike? What causes the ridge in the rim?
No.. Not an Off Center. It's called a Misaligned Die Strike. That is one of the oldest examples I have seen.
Here is some information on the difference between the two http://www.lincolncentforum.com/misaligned-die-errors-vs-off-center-strikes/