Should I use oil to stop the steaks from sticking to the grill? I tried grilling my steaks on a little sparse steel grill in a convection oven.

They came out great, with one annoying issue: they stick to the grill and have to be ripped off. This both damages the steak a bit, AND makes the grill hard to clean with the caked-on pieces of meat.

I was thinking of using a bit of oil to solve this, but don't know if it's OK?

If so, should I oil the steak, or the metal of the grill? And which oil do I use? The grill is set to 450 degrees.
I typically oil the grill.  After brushing it to get off any remnants from the last grilling session, I take a paper towel soaked in vegetable oil (something with a high smoke point), and rub my grill down with it.  (I hold it using a pair of tongs).

I then let it sit for a couple of minutes, and then rub it down again it again -- you're effectively making a plastic coating, as you do when seasoning a cast iron pan.

Now for the unbelievable part -- the next time you run into problems with it sticking ... wait.  I know it sounds crazy, but basically after a few seconds of grilling, the meat sticks to the grill ... after it's cooked long enough, it releases.  Maybe not full releasing, but it gets ... less stuck.  (assuming you're not using a sugary marinade that's turned into glue).

So long as you're okay with medium rare to medium, just give it another minute, and then try giving it a nudge to see if it's starting to release.  You won't get the cross-hatch grill marks, but most people really don't care so long as it tastes good.