What if the result of the House vote is 25-25?
The House must vote again, until it can reach a decision. If the House is unable to reach a decision by Inauguration Day (January 20), then the Twentieth Amendment states that the Vice President becomes Acting President until the House can decide.
Would this be the outgoing Vice President?
IIRC, no. The Senate could elect a Vice President, but if it couldn't, my guess would be the Speaker would be acting president.
He'd be first in line to be acting President, but he'd be insane to accept it unless he were very sure that the House and Senate would both never come to an agreement since he would have to resign his seat in order to become acting President. The same for the President pro tem. Haig wasn't as stupid as some people thought he was for saying that he was in charge until they got hold of the VP when Reagan was shot.