1
Last summer in Ibiza, we really enjoyed.
Last summer in Ibiza, we really enjoyed ourselves.
In normal sentences, enjoy needs an object. We can enjoy something or enjoy ourselves. Enjoy yourself means ‘have a good time’.
2
She really enjoys to be with you.
She really enjoys being with you.
When another verb follows enjoy, use the -ing form, not the infinitive: enjoy doing something.
3
Last Saturday, we enjoyed of the party very much.
Last Saturday, we enjoyed the party very much.
Put the object directly after enjoy, without a preposition: enjoy something, not enjoy of something.