I'm going to stiffen up my main floor joists by sistering then bridging them. In the past a friend put something in the middle, is that standard? Should I put 1/2" plywood or OSB in between?
There is no real reason to put a spacer between the joists when sistering them. Usually using some 1/2 plywood between dimensional lumber is to correct the thickness to vertical lumber dimensions, like on a header over a door. If you were to add a spacer, I would use plywood as OSB has much less sheer strength. Adding some plywood will add a bit more strength, but in your case, may not make a difference.
Both posters above are wrong. OSB has roughly double the shear strength of plywood, according to Umass Amherst and every other piece of info available easily available on the web. It also does contribute to structural strength and span limits, although there are more effective ways to increase the span strength using the same amount of cellulose.