I think these are in many cases semantically (not grammatically) interchangeable, but the nuances are as follows:
- 案外: (adverb) The situation is not what the speaker originally expected, but he is not very surprised at it. "Rather" is the closest to this.
- 意外: (na-adjective) The situation is not what the speaker originally expected, and he is more or less surprised. "Unexpected" is closer to this, I think.
One can say 「うわ、意外！」 or 「いがーい！」 after seeing something unexpected, but cannot say 「案外！」.
- 驚くべき: "Surprising", "Astonishing". It has nothing to do with someone's prior expectation. The degree of surprise is higher than the other two. (It's almost 連体詞 to me, but I'm not sure)
この料理は案外おいしい。 This dish is more delicious than I had expected.
この料理は意外においしい。 This dish is unexpectedly delicious.
この料理は驚くべきおいしさだ。 This dish is surprisingly delicious.
意外な訪問者 An unexpected visitor
驚くべき訪問者 A surprising visitor
- びっくりする: (verb) Be surprised. informal, but not a dialect.
この料理はびっくりするほどおいしい。 This dish is surprisingly delicious.
びっくりするような訪問者 A surprising visitor