A motorcycle that travels on two tires and is being ridden off highway is a Class III all-terrain vehicle. The definition does not mention the power source.
Operating a Class III all-terrain vehicle on or across the paved portion, the shoulder, inside bank or slope of any highway is the offense of unlawful operation of an off-road vehicle on a highway or railroad, a Class B traffic violation. The exemptions are a highway not maintained for passenger car traffic, an all-terrain vehicle highway access route designated by the Oregon Transportation Commission, and the cases ORS 821.200 lists for vehicles that qualify for the off-road equipment exemption, such as a highway posted to permit all-terrain vehicles, or a crossing that meets every listed condition: an angle of about 90 degrees, a place with no obstruction to a quick and safe crossing, a complete stop first, yielding to highway traffic, and a crossing at a highway intersection or more than 100 feet from one.
A rider 16 or older must hold a valid Class III all-terrain vehicle operator permit to ride a Class III vehicle on public lands. Riding without one is a Class C traffic violation.
A rider or passenger under 18 on a Class III all-terrain vehicle on premises open to the public, or on a highway, must wear a motorcycle helmet with a fastened chin strap. It is a Class D traffic violation.
A child under 16 may ride a Class III vehicle on public lands only with a Class III operator permit of their own and accompanied by someone at least 18 who holds an all-terrain vehicle operator permit and can give immediate help and direction. A child under 7 may not operate a Class III vehicle on public lands at all.
An electric assisted bicycle is a bicycle, which must be equipped with pedals and travel with not more than three wheels on the ground, that has an electric motor and is a Class 1, Class 2 or Class 3 electric assisted bicycle. Class 1 assists only while the rider pedals and Class 2 may be propelled by its motor without pedaling, both ceasing at 20 miles per hour; Class 3 assists only while the rider pedals, ceases at 28 miles per hour and must have a speedometer.
This page restates state law in plain words and links the text it came from. It is not legal advice. Cities, counties and the agencies that manage federal land (the Bureau of Land Management and the Forest Service) add rules of their own, so check with whoever manages the ground you plan to ride.