Is it permissible to dispose of the electrical appliances and network devices that were bought to help one's nephew get married, especially given the debts incurred from this assistance, and after the couple has left her home?

The questioner's spending on her nephew is a good deed. Her disposing of what she gifted him depends on her intention. If she intended merely to permit its use, then it remains her property, and she may take it back whenever she wishes. If she intended charity, then she may not retract it or demand compensation for it, unless he had not yet taken possession of it. As for if she intended it as a gift: if she did not intend compensation, she may not demand it or retract the gift. If she did intend compensation, she may demand it, and it is the value of the gifted item on the day of possession. If the recipient refuses to pay, she may retract the gift. If she made no specific intention, then she may not demand compensation or retract the gift. If she specified a known compensation, it is a sale. If the compensation was unknown, then the gift is void, and the property remains in the possession of the giver. The reason for not being able to dispose of the gifted item after its possession is that it leaves the ownership of the giver and enters the ownership of the recipient. If the recipient refuses to give compensation, the giver may retract the gift itself.