Of course it depends on the situation.
Antinukes buried too far down collide with the hole walls and EMP aoe is large enough to hit through small holes or walls. It is balanced such that you cannot have invulnerable antinukes.
Against Inferno shield blanket is very effective as Inferno has almost no direct damage. The fire will still seep into the shield but that should be in the air if you have a blanket. Single shields are less good against Inferno as the damage can sneak in the sides if aimed next the the shield.
Shield is also very good against tacnuke. A single shield will block a tacnuke when near full charge and shields cost less than a single tacnuke missile.
EMP missile goes right through shields. This is not inconsistent behaviour as shields block projectiles that have less damage than their current charge and EMP missile has more EMP damage (counted as damage for the purpose of shields) than shield max charge.
Cloaker is the other counter to deep base strikes. It is good against EMP and Tacnuke as they need targets to be cost effective but not so good against Inferno as it has a pretty large AOE.
As for antinuking I can think of 4 broad methods off the top of my head.
1. Spread out. As Skasi said their nuke is pretty worthless if they need to kill more than a few areas on the map in order to not lose. This is of course dependant a large map.
2. Make antinuke beyond tacnuke range. Tacnuke's only have around 3500 range so if the map is large enough you should be able to keep enemy tacnuke emplacements far enough away from your main base. These tacnuke places are not cheap to set up.
3. Always have more antinukes than your opponent knows about. Cloak every antinuke and take note of antinukes that have been scouted, for example during construction or by a Spy.
4. Make more antinukes when you need them. If you have 3k metal in storage and 13 Nano Turrets you can produce an antinuke in under 20 seconds. If your current antinuke is emped or destroyed immediatly build another and you should have enough time to intercept the nuke.
The top 2 strategies are more useful in teamgames while the last 2 are for FFA mainly due to the differences in base density and income.