Can you adjust the placement of the slide? I'm wondering if it's a jar opener: adjust the slide to fit the lid, clamp closed, turn. We have a similar device with an open frame that's been handy at times.
Not sure what the two prongs on the other side are. I'd speculate that the prong on the end was probably originally vertical to the body of the tool, like the prong on the slide. What that did, though, not sure. Maybe clearing out nostrils for people with severe head colds.