There was a time when I tortured animals, long ago and someone told me I have to pay damage to the owner, but I don't know the owner and there is no way of finding out. How do I deal with this?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Dear brother, you should know that torturing animals is forbidden in Islam. The Prophet informed us that Allah put a woman in the Hell-fire due to her mistreating a cat. The Prophet said: "A woman was tortured and put in Hell because of a cat that she had kept locked up till it died of hunger; she neither fed it nor watered it. Then she locked it up, nor did she set it free to eat the insects of the earth" [Reported by Imams Bukhari and Muslim].
The Prophet also said: "May Allah Curse the one who makes any soul a target (of pelting) " [Reported by Imam Muslim].
Thereupon, you have to repent from this sin, and for a valid repentance return the rights of the person that were violated, if any.
Thus, if the animals you have tortured were useful and were to be sold you have to pay their owners the value of those animals. If you do not know the owners then you should give an amount equal to the price of the animals in charity, intending that the owners will receive the reward. Afterwards if you should meet the owner you inform them about the giving to charity. If he accepts it, you are freed of any responsibility; otherwise, you have to pay them their rights.
Allah knows best.