When I met the sphinx I got into a slight altercation after answering one of his questions incorrectly (Anephas instead of Kerah). The outcome, after losing my rogue and a relaxing dip in the lagoon to replenish my HP, was an all-in brawl (he was backed-up by wyv wizards and pirates). Afterwards there was a dead sphinx from which my characters gained quite a few XP.
Thinking of Wyvern's warning that we should not kill such pleasant characters, I had a rush of morality (or panicked that I couldn't finish the game) and dutifully loaded the last save. I then gave him the correct answers that spang to mind after visiting Ironworks. He then proceeded to disappear after spitting in my face...no keys, nothing.
Q. CAN I KILL THIS GUY WITH IMMUNITY? Or do I HAVE to be nice to him?

Mattman

I don't think you have to be nice to him. If you answer the questions correctly he'll open up Anephas' tomb. If you get the answers wrong I think you have to possess the Lich's staff of death and use it on the entrance to get into the tomb.

//J

As I recall, the Sphynx doesn't open up the tomb for you whether you answer his questions correctly or not.
I rather like the Sphynx but he is worth a lot of experience points (booooo on the designers) so many players have offed him.

Wyv

I have never set out to slay the sphinx, but I have yet to answer all the questions correctly....

I have seen no ill effects from it. I wish there, were, or a bonus of some sorts for answering the questions.