The Register-Guard of Eugene, Oregon, has this op-ed by Sal Peralta, Secretary of the Independent Party. The party recently obtained enough registrations to qualify for its own government-administered primary. Generally, minor parties in Oregon nominate by convention, although as the op-ed explains, the Independent Party has been conducting its own primaries at its own expense in the recent past.
Other states that now have a ballot-qualified party called the Independent Party are Connecticut, Delaware, Florida, and Hawaii. States that had a ballot-qualified party with that name in the last forty years are Maryland, New Mexico, North Carolina, South Carolina, and Utah. At any time, anyone is free to complete the paperwork to have the Independent Party recognized in Louisiana; that just takes someone to pay a fee to the state of $1,000.