In Maoz Tzur we say:
רב בניו וקנייניו,
על העץ תלית
His many sons and his possessions,
You hung on a tree
Were Haman's possessions really hung on a tree?
It's amazing what you can find on Hebrewbooks!...
In Sifsei Chachamim, by R' Avraham Abba Hertzel (Bratislava, 1899), he says that this is based on the Gemara's statement (Megillah 15b, top) that "that wicked man had all of his treasures engraved on his chest" (evidently meaning that he wore a medallion, or something similar, that had all of his possessions depicted or listed on it). Presumably he would have worn this to the two feasts to which Esther invited him, and since he was taken directly from the second one to be hanged, then that medallion - "all his treasures" in microcosm - was hanging there on the gallows with him.
The translations I have seen translate it differently, and effectively elide the vav; either קניניו refers to the rest of Haman's household, or to the fact that his sons were his dearest possessions.
which means: "His multitude of sons, his dear treasure, were hung on his own gallows."
which means: "His most precious property, his many sons, You let hang on the gallows."
Perhaps you can break it up like this (M'layl)- you wiped out the enemy of his name (including) his many children and possessions, you hung him on a tree.
In Riv'vos Efrayim (volume 8 number 267), Rabbi Efrayim Greenblatt suggests that it may refer to Haman's slaves. (He also refers the reader to Or L'avraham on Rus, by Rabbi Avraham Gurewitz (spelling?), page 98; but I don't have a copy.)