As has been said before, it's impossible numerically for him to get the nomination and with so few delegates, he'll barely have any influence at the convention. The best he could hope for is maybe a cabinet position (not sure what he'd be interested in) in exchange for the delegates.
No man, you are thinking about this wrong. Kasich basically gets a mulligan on the first half of the race. Now he gets to run in a three man field for the second half of the race. He is an underdog due to the lack of money and organization. On the other hand unlike Trump, Cruz, Bush and Rubio, most republicans dont loathe him. It's sorta useful to not have a majority of the voters not hate your guts.
Kasich isn't going to catch up with Trump, that is a mathematical uncertainty. What Kasich needs to do is deny Trump a popular mandate and be able to claim that the republican base has rallied around him. And it helps his cause that April is full of states he wants to run in. Next up is Wisconsin where he is a very serious contender with Rubio gone. Three weeks after that we've got Colorado, Pennsylvania, New York, Connecticut, New Hampshire, Delaware, all liberal states where his brand is going to have a shot. There aren't any more southern states. The story at the end of April could be "Kasich, the man who healed the wounded republican party."
If Kasich can go to the convention with 500 delegates and get a contested convention he would be a very strong favorite in the negotiations with party elites. Trump would have more delegates but Trump would be reeling from three months of failure while Kasich would be on a high from 3 months of victory. People would forget about the early contests, write them off as the product of a divided field.
It's a highly, highly, highly unorthodox situation. But primary contests with a lot of candidates have extraordinary results from time to time. It requires that Kasich really kick some ass. He needs to build a Wisconsin organization from the ground in three weeks and build a new England organization from the ground in six weeks. But he will be doing that with a natural constituency. Look at Sanders competing in Nebraska and look at Jeb Bush failing in New Hampshire and you will see how much of a difference having a candidate with a pulse and a narrative helps in building an organization. So it's a longshot but it's less of a longshot then it was a week ago.