We have a very serious problem along a 175' stretch of ground on the Umatilla River in Umatilla County. They have intruded 30' of our land. How do we get rid of them without trapping since trapping is not a permanent solution. Thanks Dave
Umatilla County Oregon
Thank you for your question. This sounds like a challenging situation. Is the main damage occurring via bank burrowing? I am guessing so, given the length of the frontage you mention. I highly recommend this publication as one that can help with some preventative bank improvements to decrease and deter burrowing. http://icwdm.org/handbook/rodents/ro_b61.pdf The same article has some excellent figures and advice for trap-setting. You're right - Trapping has only temporary effects, but you might need to employ that tool along with others to manage this issue over the long term. Muskrats are a managed furbearer species in Oregon however, so you need to get the proper permit (via ODFW) and do the required reporting (how many animals removed) if you employ any population control techniques.
As a first step however, I would get in contact with your Or Dept of Fish and Wildlife (ODFW) District Biologist. S/he should be a great resource in getting some direct assessment of the magnitude of your situation. You can call ODFW headquarters Main Phone (503) 947-6000 or (800) 720-ODFW 
to get the name and contact number for your local District Bio.
Another option to consider would be an ODFW-trained and certified Wildlife Control Operator ( see list http://www.dfw.state.or.us/wildlife/license_permits_apps/wildlife_control_operator_contacts.asp) These are private contractors who help land- and home-owners with prevention and management of wildlife damage and conflicts.
I hope this information is helpful.