What did Eleazar the priest need 32 virgin young girls for?

Sigh- it didn't all go to Eleazar- he accepted the tribute (including the people) as representative of all the Kohanim and then it was further divided amongst the Kohanim and Levi'im as the Terumah offering.

Later, under circumstances not recorded, Balaam became involved again with the Moabites. He would not curse Israel for Moab's sake, but he did inform the Moabites that the Israelites would lose the grace and strength of the Lord only as they sinned. Thereafter the Moabites and Midianites enticed many Israelites into idolatry and adultery until a plague struck Israel, taking twenty-four thousand casualties. Finally Israel repented and fought against and prevailed over the Midianites. One casualty of the war was Balaam, who was killed by the Israelites. (Num. 31:16, 8; 25:1-9, 16-18; 31:1-20.)

Smith's Bible Dictionary, William Smith, 1884

Booty consisted of captives of both sexes, cattle, and whatever a captured city might contain, especially metallic treasures. Within the limits of Canaan no captives were to be made, Deuteronomy 20:14, 16; beyond these limits, in case of warlike resistance, all the women and children were to be made captives, and the men put to death. The law of booty is given in Numbers 31:26-47; As regarded the army, David added a regulation that the baggage guard should share equally with the troops engaged. 1 Samuel 30:24 5.

They became servants.

And btw: in Judaism you are not allowed to sleep with your servants.