Is it permissible to eat food that I swore by Allah not to want, then later desired it, and what is the expiation for that if I am unable to feed ten needy people but am able to fast?

If you swore by Allah not to ask for or eat two specific foods, then you asked for or ate one of them, you have broken your oath, and expiation for breaking an oath is required of you. Fasting is not sufficient expiation for breaking an oath unless the person does not have enough left for their sustenance and the sustenance of their dependents after the cost of feeding or clothing, or if they are among those who are permitted to receive Zakat (definition).