I live in Oregon and I would like to evict my boyfriend from my rental property for several reasons. He does not want to help with the bills but would rather spend his money on alcohol and drugs. I would really like to get him out of my life.

He is renting from you, or he is living with you in the property you are renting? Do you have a formal agreement with him? You need to determine if you are (by default) his landlord - or if he's on a lease with you then it would be up to your landlord to evict him.

There's a link in a sticky at the top of this forum to each state's landlord / tenant laws. Depending on the exact situation, you'll need to give him notice to leave and then if he doesn't you'll have to file an eviction case against him.

He is living with me. His name is not on the rental agreement or any of the utilities. Any advice?

Then the scenario would most likely be that you would be in the landlord position and he the tenant. You can follow your local / state eviction proceedures. Go check out the state laws.

If you had a payment agreement with him and he hasn't adhered to it, you can follow the proceedures for non-payment. If there was nothing really set about payment arrangements then the safe bet would be to terminate his "periodic tenancy" (month-to-month) by giving him the necessary notice (usually 30 days - varies by location) to vacate. Then if he doesn't leave you go through eviction.

Do everything in writing, so you have the necessary proof if it winds up in eviction court. And once you start the process it's best to lay low and not have a lot of conflict with him. You don't want him having any ammo against you that he could present to the judge.

This looks like a good place to start:
Landlord and Tenant Law (http://www.osbar.org/public/legalinfo/tenant.html)