Thanks for the kind explanations, Decimus san and Masaegu san.
There is something which I am still not sure about which is should I use 誘うor 呼ぶ when telling someone that I was invited by the inviter who is the host/sponsor of the event.
For example:
私はスミスさんにカラオケに誘われました。
or
私はスミスさんにカラオケに呼ばれました。