California and Oregon are both members of the Drivers License Compact (DLC) so the California ticket conviction will be reported to Oregon's Department of Transportation.

It would seem from the information given in the Reciprocal agreements and interstate compacts section of the Oregon Revised statutes (ORS) 802.500 to 802.540 that the CA, or other out of state tickets will be placed on your OR driving record. In this ORS section it basically states that Oregon must treat out-of-state conduct the same as it would treat in-state conduct.

Traffic violations remain on Oregon driving records for approximately 10 years from the conviction date, according to DMV. Oregon does not operate on a "point" system for traffic offenses.

You can quality for traffic school in the state of Oregon if all of the following apply:

• If you have not received a citation within the last three years
• If you have not attended traffic school in the last three years
• If an accident was not involved
• If the citation was not issued in a highway work zone or a school zone

As you already mentioned you do are not eligible for traffic school so the tickets you received in and out of Oregon will be placed on your driving record. DMV will revoke your driving privileges for five years if you are convicted of three or more of the following offenses within a five year period:

• Any degree of murder, manslaughter, criminally negligent homicide, assault, recklessly endangering another person, menacing or criminal mischief resulting from the operation of a motor vehicle.
• Driving while under the influence of intoxicants.
• Driving while your driving privileges are suspended or revoked.
• Reckless driving.
• Failure to perform the duties of a driver after a collision.
• Fleeing or attempting to elude a police officer.

DMV will also revoke your driving privileges for habitual offender if you are convicted of 20 or more traffic violations within five years. To view a list of types of traffic violations for 20 or more convictions, see Oregon Administrative Rule (OAR) 735-064-0220.

The Oregon's driver's manual also notes that if you have three convictions, or three accidents, or a combination that totals three, in an 18–month period, DMV will restrict your driving privileges for 30 days. The restriction will not allow you to drive between 12 midnight and 5 a.m., unless driving for work purposes.

If you have four convictions, or four accidents, or a combination that totals four, in a 24–month period, DMV will suspend your driving privileges for 30 days.

From this information it would appear that your driving privileges could be at risk due to the amount of tickets you have received within a relatively short period of time. To find out for certain what penalties you may be receiving against your driver's license check with the OR DOT.