Q. Is the house considered a gift or inheritance?
A. Simple answer: inheritance.
The usual rule, for a gift, is that the recipient's basis is the giver's basis (what you father paid for it). But there is an exception for the gift of his home, where he retained the right to live there ("life estate"). "If you give away an asset and keep a life estate in that asset..... the cost basis of the house is "stepped-up" to the value of the house on date of death [IRC 2036]")
More info: http://www.law.cornell.edu/cfr/text/26/20.2036-1
A life estate does not have to be explicitly established in the deed. Your father probably had an "implied life estate." If so, that would give you the stepped up basis. There is case law on this.
Q. I intend to pay off my own mortgage with the proceeds of the sale. Is there a penalty or benefit for doing so?
A. No. Paying off the mortgage is irrelevant, for tax purposes. It does not change the amount of the gain.
Considering expenses of sale, most people have a loss, on the sale of their parent's home.
Q. Is that loss deductible?
A. Yes, most likely. If the house was "investment property", and sat vacant between the time you inherited it and sold it, you can deduct the loss. If it was personal use property (you or your siblings lived in it), it is not.
