Public Policy Polling surveyed Ohio Democrats and Republicans on their presidential preferences between June 4th and 7th. About 360 Democrats were queried (with a 5.2 point margin of error), and 411 Republicans (with a 4.8 point margin of error).
In the Democratic race, Ohio looks just like the other states polled so far. Hillary Clinton has a huge lead. The only significant thing is that, at least so far, Sanders has been unable to cut into the Clinton lead (even among the liberals, where he hoped to get the most support). Biden and Warren were not included in the poll -- probably because Biden has expressed no real interest in running, and Warren has made it clear she will not run.
The GOP survey is a little different, because Kasich comes out of low single-digits to lead the pack. That is to be expected, since he is a fairly popular governor of the state. He has to be disappointed in getting only 19% though. That could be enough to get him all of the state's delegates -- since he successfully moved the Ohio primary back to make it a winner-take-all primary. But his problem lies in other states, where he has shown no ability to get votes (at least so far).
Public Policy Polling is currently doing a new national poll (they do one monthly), and it will be released in about a week.