-- Last Updated: Jun-21-13 2:09 PM EST --
grips are holding up quite well. However, while I think oiled shafts or blades weaken the wood, this isn't a consideration with wooden grips. An oiled grip gives a little better "traction" and feels friendlier.
I use Minwax 209 clear for oiling grips. After sanding the grip smooth, I actually wet the surface with water to raise and open the grain. I apply multiple coats of 209, wiping off the excess, and waiting until the oil seems dry (by touch and smell) before the next coat.
I keep going until the surface appearance indicates that the grip isn't taking any more oil. Then, using maybe 400 sandpaper, I wet sand the surface using 209 as the "wet", and wipe down the final time.
Oil doesn't penetrate very far, and in use, the grip may show patches that look "dry". Don't worry about them. You can just apply more oil some rainy weekend when you're not paddling.
Others will have their own OCD approaches to oiling...
This link shows a custom grip (elm) that is oiled. It may look varnished, but the satin surface without "depth" is how a thorough oil job will come out.
Recreational Kayak Paddle