My husband is a US citizen of Costa Rican descent. Before she died, my mother-in-law (NOT USC or LPR) signed her house over to my husband. She died shortly thereafter and now he is selling the house and will divide the money among the heirs. Some of the heirs are US citizens (like my husband) and live her; some are Legal Permanent Residents; some are neither citizens or residents of the US and live in Costa Rica.

Does ANYONE owe taxes on this money? Would it be different if the house had been left to the family in a Will?

Thanks!

The house was a gift. Since your mother-in-law is NOT a resident or U.S. citizen, the gift tax does NOT apply to her.

No taxes are due from anyone.

Doesn't the IRS require that US citizens report and possibly be taxed on any capital gain when a gifted house is sold? Or if there is a loss wouldn't there be the possibility to claim a tax deduction?

As ATE states, there is no gift tax involved.
However, if there is a gain on selling the house, you might have to pay taxes on that , depending how high the gain and if that was your primary residence.
You need to determine the basis of the house. This is done differently for gifted and inherited property. See here:
Tax Basis of Inherited and Gifted Property - FindLaw
You can exclude up to $250000 of gain from being taxed. Have a look here.
And of course take into account that the money was shared, so not the entire money is attributable to you/your husband.