You would use intrigued with to imply making secret plans to do something evil; for example, "the group was intrigued with malice." On the other hand, intrigued by shows arousal of interest or fascination. An example would be: "He was intrigued by the sentiments on TV."

The entire family was intrigued.

The opposite of intrigued (not intrigued) could be uninterested or bored. The reverse reaction would be repulsed or repelled.

Intrigued is a verb. The noun form is intrigue.

Science had always intrigued her, so she decided to major in chemistry and biology.