If the arrest was recent
Start with the county jail
In Oregon, someone who was just arrested and not released is held in the COUNTY JAIL run by the county sheriff (Oregon has 36 counties), not a state prison, so the Oregon Offender Search will not show a brand-new arrest.
Oregon participates in the national VINE system (Oregon VINE), a free way to check custody status and register for alerts by phone, email, or text (search at vinelink.com).
Many Oregon county sheriffs also post an online jail roster or 'adults in custody' lookup (for example, Multnomah, Marion, and Deschutes counties).
For a very recent booking or bail information, call the county jail's booking or records line.
Jails are run by the sheriff in each of Oregon's 36 counties, and many post an online jail roster or 'adults in custody' lookup. Use the county sheriff's roster or Oregon VINE, and call the jail's booking/records line for a recent booking and the bail amount.