Is it permissible to perform Hajj on behalf of a deceased person using their money by sending a stranger to perform Hajj on their behalf, when there are relatives who are able to perform Hajj on their behalf? And is donating the money to poor Muslims or to da'wah organizations better than performing Hajj on their behalf?

It is not a condition that the proxy performing Hajj on behalf of another be a relative. It is permissible for someone who has performed their own obligatory Hajj to perform Hajj on behalf of another. If Hajj was an obligation upon the deceased, or if they willed it and the expenses were within one-third of their wealth, then Hajj must be performed on their behalf. However, if it was not obligatory upon them and they did not will it, then it is better to donate the expenses to the poor and needy who are facing hunger or religious strife, or to support da'wah (inviting to Islam) and spreading Islam, because the benefit here is far-reaching. It must be noted that the deceased's wealth, after their death, transfers to the heirs, and it is not permissible to perform Hajj on their behalf from the inheritance money except with the consent of all adult heirs.