You can use any muzzleloader (scoped inline, traditional, etc) during any rifle hunt.
You can use an inline on a designated muzzleloader hunt but it has to meet the restrictions, ie open ignition, no pellets, sabots, centerfire primers etc...
I've used my flintlocks to take a couple of bear over the last few years during the general bear season. Weather is better, nobody is hunting anything else yet and the trout are biting.
Oregon doesn't have an "Oregon Muzzleloading Association" that I'm aware of. There is a state shooting organization (OSSA) that could be considered an umbrella organization, but they rarely even mention muzzleloaders.