Yes. You report the full amount on your Oregon return.
You must report these winnings on your Oregon state tax return. The program should import the income from your federal interview.
Oregon does exempt winnings of less than $600 from the state lottery, but all other gambling income is taxed.
You will not owe in North Carolina because you won after moving.
Source: https://www.oregon.gov/dor/faq/pages/default.aspx
