I'd say just killing blow gives extra exp for sure, since if you play the whole game with a combo pattern where the same guy always ends up with most kills you'll definitely find him/her at several levels higher than the one who always does the first strike (supposing you level a fair bit, anyway). I think it may also be necessary to attack at least once to get "normal" exp as I've had some setups where someone doesn't seem to level at all because I haven't been paying much attention to enemy hps and one guy never gets to attack orso.
I've got the best results at leveling when I consistently pay some mind to it so that for instance in a 3 mob encounter, char1&2 attack mob1 (char2 gets kill), char 3 attacks 2nd mob, not killing it -> next turn char 1 attacks mob2, killing it, char2&3 attack mob 3, char3 gets kill -> everyone gets a kill.
The lack of visible exp counter and enemy hp are a few things that one can hope were fixed in the sequels.
Phlebas the Phoenician, a fortnight dead, Forgot the cry of gulls, and the deep sea swell // And the profit and loss.
- - Gentile or Jew // O you who turn the wheel and look to windward, Consider Phlebas, who was once handsome and tall as you.
[T.S.Eliot: The Waste Land - IV. Death by Water]