If I understand my physics correctly, (and BTW I know demolitions pretty well) The problem with blowing up a mass that size in space is NOT the tonnage of explosives. Its the very nature of space itself. The vacuum negates a rather larger percentage of the impact value of the explosive charges. Personally if I were going to attempt to deviate a chunk of rock, I would employ the bunker buster method and drive the explosive deep within the rock before detonation.

The problem with our nuclear arsenal is its designed for atmospheric detonation. We would need to create a different deliver system to effectively harness the power of nucleonics in any attempt at Texas sized chunks of rock.

Even though any munitions that could be delivered to the asteroid wouldnt cause any noticable damage, they could take it off course if used correctly. A bunker buster type bomb would be effective since it would send a stream of ejecta out of the side of the asteroid, thus imparting a fair amount of momentum to the asteroid (more than would be possible with a surface detonation). Done early enough, and with the correct angles, this could push the asteroid out of Earths way. The technical challenges would be pretty big tho, youd have to do NASAs Deep Impact mission all over again but with a completely redesigned impactor, strong enough to penetrate the asteroid surface and survive long enough to trigger detonation. This sort of thing hasnt even been considered by the armed forces of the world as far as I'm aware, so would have to be designed from the ground up. Also, as Underdog said, current nuclear warheads probably couldnt detonate in vacuum, a new system would have to be devised.

Giant trampoline?

I say that you should install a bunch of engines on it early enough (probably conventional ones rather than ionic), then capture and mine it to recoup the costs. There's no point in blowing it up, though perhaps you can explode some bombs in front (preferably with as much momentum as possible aimed towards the asteroid) to help slow it down further and set its course so that it's captured by the Earth's gravitational field.

Lep, planting engines on it could work but current technology isnt sufficient to either plant engines on an asteriod powerful enough to alter its course, or mine an asteroid.

Underdog, nothing is in permanent orbit. Space is not a perfect vacuum, therefore there is (very small) frictional resitance to bodies travelling through space. I beleive one of the moons of Neptune is going to collide with the planet in a few thousand years, and Earth's moon is slowly drifting away. Forcing an asteroid to collide with the moon rather than Earth is not only more difficult than making the asteroid simply avoid Earth, it is also potentially more dangerous, as there could well be moon bits falling out of the sky for years afterwards.