What is the ruling regarding a son building on his father's land without the father's permission or financial contribution, especially given that the father swore by triple divorce that if he (the son) builds on this land?

The validity of an oath is based on the intention of the swearer. If your brother intended that no construction whatsoever should take place on the land, and his son built on it, then your brother has broken his oath, and his wife is divorced thrice according to the majority of scholars, contrary to Ibn Taymiyyah, who holds that only an expiation for the oath is required. There is no consideration for trickery in an oath. However, if he intended that he himself would not build, or that it would not be built with his money, then there is no harm in his son building on it with his own money, provided his father gives permission if he is the owner of the land, as it is not permissible to dispose of another's property without their permission. We caution against swearing by divorce and against making it a means to solve problems. Your brother should consult trusted scholars.