The Oregon Judicial Department's Website has a court calendar search function.  You can search by court, party name, date, and/or attorney.  You can also view customized calendars for each circuit court. If you have questions about a court's calendar, contact their calendering office.

All Oregon County Circuit courts (and most if not all county, justice, and municipal courts) allow free on-site (in the courthouse) access to OJIN (the Oregon Judicial Information Network, a database of docketing information for Oregon courts). Some may only allow access to records filed in their particular county.  You can search OJIN to see the activity that has occurred on a particular case (such as trial dates, documents that have been filed, etc.).

Few if any public libraries will subscribe to OJIN.  It is not an easy database to use, due primarily to the fact that it was designed many decades ago for court staff and lawyers. Keep in mind that few full-text documents are in OJIN.  If you need copies of actual documents filed in a particular case, rather than just reading the docket entry, you might have to go to the courthouse file room or clerk's office anyway, so remote access will not save you a trip to the courthouse.

Some county law libraries have OJIN subscriptions. Contact your local county law library to find the best access for you.