Is it true that building houses and assisting in it yields no reward, based on the saying: "Stone upon stone yields no reward"?

What you heard from the Imam is not absolute. Building mosques is among the things encouraged by Islamic law, as is building homes for the poor and needy, and a person building for his family what protects them from heat and cold. All of that carries reward and virtue.

The hadith, "Whoever builds a structure more than he needs, it will be a burden upon him on the Day of Resurrection," is very weak. Even if it were authentic, it would be interpreted as building in excess of need with the intention of showing off and gaining repute, or merely for pleasure and expansion.

As for the hadith, "Every expenditure a servant makes, he is rewarded for it, except for building," it refers to building for purposes other than a mosque, or what is in excess of need. Mosques and what a person needs are not included in the building that is exempted from reward.