I had a refugee family living with me for most of the year. Can I claim them as dependants or have them as a deductible somehow or charitable contributions?

No. For someone that is unrelated to you, they must live in your household for the entire 12 month. There are additional requirements, but the fact they didn't live with you the entire year disqualifies them as a dependent.

For more information on claiming a dependent, please see this TurboTax Help Article or IRS Publication 501.