I relocated for a new job, 1st into temporary housing (paid by employer), and then into a house we bought. Are both moves (to temporary and permanent houses) deductible?

Yes, you will be able to claim all moving expenses relate to a relocation or new job move if the your original move meets the IRS eligibility requirements. You will be able to deduct moving costs up to a year after your move.

When inputting your move information, just make sure to use your permanent address as your final move destination (and include the cost of your temporary housing as temporary lodging costs related to your move).

According to the IRS, if you moved due to a change in your job or business location, or because you started a new job or business, you may be able to deduct your reasonable moving expenses but not any expenses for meals.

Please refer to these links related to moving expenses: IRS - Moving Expenses and Moving Expense Deduction