All of them would be understood, though there some nuances

• The first one “J’y ai été.” is fairly common, though incorrect according to traditional (prescriptivist) grammarians who insist that you should say either “J’y suis allé” or “J’y étais” instead. It is perceived as a common mistake, intensively frowned upon, especially at school (have to cull it out early) and thus sounds rather familiar or uneducated (again for those who care). Use it at your own risks, but be aware that in popular settings, using the canonical “J’y suis allé” might make you sound posh.
• The second one shares the stigma of the first one, without having its brevity. It would be understood too, but would sound a bit awkward to a native speaker (at least this one).
• The third one is very correct, borderline fancy, but since you are not a native speaker, you might go away with it.

As for the choice of tense: in an answer to a direct question, staying close to the question is usually a good idea, so yes, better use passé composé, though imparfait “J’y étais.” would work, too. “J’y allais.” would not, though, since it would imply that you tried to get there, but couldn’t make it.

IMHO, the imparfait would be more grammatically correct, as being at a party normally lasts some time. But the passé composé always replace the passé simple in spoken language, and can even replace the imparfait.

In familiar/spoken level I would say:

— T’es allé à la fête hier ?
— Oui, j’y suis allé

While in formal/written level, I would use:

— Étais-tu à la fête hier ? (ou Est-ce que tu étais à la fête hier ?)
— Oui, j’y étais.