Actually, to clear things for Lonefire, the effect still activates and resolves on the field, regardless of what you tribute, but Skill Drain doesn't care where the effect activates or resolves - it cares whether the monster who activated the effect is currently face-up on the field when the effect resolves. If the monster is not face-up on the field during resolution of the effect, then Skill Drain will not negate the effect.
EDIT: A quick note on Debris Dragon, since that was part of the question. Debris Dragon's effect to special summon a monster WILL be negated by Skill Drain. What won't be negated is his conditions on what can be synchro summoned using him. Aka, Skill Drain does not allow you to use a level 4 monster with him and does not allow you to summon a non-Dragon-type monster with him. That is because those are conditions on the card, not effects.
As for Rai-Oh, his effect to negate a special summon will not be negated by Skill Drain because he tributes himself as a cost and is therefore no longer on the field when his effect resolves. His effect to stop players from adding cards to their hands will be negated by Skill Drain.