Is it permissible to give interest-based gains acquired from usurious banks to one's parents, paternal uncles and aunts, or relatives in general, whether they are well-off or not, and how can one dispose of it to ensure not bearing its burden?

It is not permissible to acquire ownership of usurious interest. It must be disposed of by spending it on the general welfare of Muslims or by giving it to the poor and needy.

If your relatives are poor and in need, it is permissible to give them from it. However, if they are well-off, it is not permissible.

As for parents, if they are well-off, it is not permissible to give them from it. If they are poor, their maintenance is obligatory upon you, and it is not permissible to give them from the interest unless you find no other means to spend on them. In that case, it is permissible to spend on them and on yourself to the extent of need, because the poor person who benefits from it owns it as a lawful and good possession.