Yes, there are California car insurance companies that will insure you, though your car is still registered out-of-state in Oregon.
Keep in mind that California car insurance Liability limits are set at 15/30/5, while Oregon's limits are higher at 25/50/20, so you will need to keep these higher limits on your car during the period it still registered in Oregon. Also, make sure Oregon accepts your California car insurance policy.
The issues you may run into aren't likely to be with obtaining California auto insurance, but with the state of California since they require you to change over your title and registration within 20 days of entry or taking up residency in California.
If you fail to register your car during the given time frame, California can penalize you, which means if you wait till November to register your car you will likely have penalty fees on top of your regular registration fees.
If you have not yet changed over your driver's license you need to do so soon as well. California gives new residents who move to their state only 10 days in which to exchange their out-of-state license or else if you are pulled over and found to be a resident of California, you can be cited for driving without a license.
When shopping around for low cost car insurance in your new state of California, come to CarInsurance.com, an online auto insurance marketplace. We offer you the ability to shop for car insurance online and the ability to purchase your policy directly through CarInsurance.com.