We moved over 400 miles for a new job. While we waited to sell our house, we had temporary living and were given a per diem. Do we pay taxes on that per diem, or can we deduct actual expenses? Employer included it in income and we did not have to submit expense reports.

Yes, the per diem IS taxable because it was given to you under an "unaccountable" plan.

Unfortunately, the lodging and daily expenses during a move are NOT deductible as moving expenses on Form 3903. You CAN claim the lodging cost for the FIRST night in the new town, but that is all.