In the State of Oregon if I marry my boyfriend can I be held equally responsible for the child support of his child from a previous one night stand?

It depends on your states law. This may help you a bit
https://www.askmehelpdesk.com/marriage/marriage-child-support-248338.html
Since it may be hard to find the answer.
For the most accurate current answer it would be best to call your local child support, domestic relations, family court and ask them.

I am not sure about Oregon so I would recommend the same as nohelp did the local family court or family law office will know and should be able to tell you over the phone (no charge).