Is it true that in the State of Oregon a 10 year old child can choose which parent they would rather live with
NO, it is not true. In MANY states, minors (of varying age) are ALLOWED to talk to the judge, and express a preference. The judge still has the final authority to make the decision.
The law (anywhere) is not going to be so dumb as to (hypothetically) let a child chose a parent who might be a registered sex offender, because that parent lets him have pizza every night for dinner. Children have opinions, but they really don't have the maturity to know what is really in their best interests.
Never heard of ten year olds, but I have heard that it is the fourteen year olds , who can choose.