The recipient of a gift never pays tax**.
The giver is required to file gift tax return form 709 when the person makes a gift of more than $15,000 per person per year. This form is not part of a regular tax return (and Turbotax does not prepare this form) but it is due the same day, April 15. Gift tax is not owed unless the giver's lifetime total gifts are more than $11 million, but form 709 is filed to track a person's gifts agains their lifetime limit.
I would ignore the truck. Essentially, the son sold the truck for his mother. It wasn't really a gift if he gave the mother the proceeds.
The mother gave each son half a house. Assuming the value of the house was more than $15,000, the mother must file form 709 to report the gift. But she won't owe gift tax, and neither will the sons.
(**One of my nitpicking friends may point out that if gift tax is owed and the giver does not pay it, the IRS can collect from the recipient. This is an uncommon situation, and here it seems very unlikely that the mother's lifetime gifts are more than $11 million.)
