To be able to control earthquakes and volcanoes, we have to first understand them. We do not fully understand either. Actually, we know very little about both of them.
Our current understanding of earthquakes involves several mechanisms. The most common are due to plate tectonics where either plates are moving apart, squishing into each other, or moving past each other. Unfortunately, there are earthquakes in places where none of those mechanisms fit (such as the New Madrid fault zone).
Our understanding of most earthquakes is that they happen where some fault zone has stopped moving and the underlying plate is still moving. At some point, the movement of the underlying plate puts enough stress on the point that isn't moving to break the rock that is holding the fault stuck and the fault moves. It can move fast enough to actually melt the rock by friction.
So, for these earthquakes, you would need to invent a technology that can:
1. find where the fault is building up stress
2. Get down to that point (10-80 km below the surface)
3. 208
Perform some action to start the fault moving again
There have been man caused earthquakes. Most of these have been caused by injecting waste water deep into a fracture zone at high pressure. We do not know how that fluid moved to the earthquake epicenter nor what the mechanism that triggered those earthquakes. All we know is that when we pumped that stuff down, more earthquakes happened nearby.
Also, we are still experiencing earthquakes on faults we didn't know were there.
Likewise, with volcanoes, we would need to know how to predict them, how to measure the signals that something is happening, and then need to invent some technology that can harness that huge amount of energy release. It has been only in the last few decades that we have been able to do any prediction of volcano activity. Yet, with all the tools we have today, an Alaskan volcano gave less than 24 hours notice before erupting.
To simply harvest some of the energy of a volcano, think of how much heat is produced by one. Volcanoes are driven by mantle heat and the eruptions are partly due to water and CO2 changing from super pressured liquids into gas. Some estimates are that we could take a trillion watts of power from Yellowstone but the water requirements would be huge.
Frankly, we would not want to cause eruptions, we would want to stop them. Pulling the heat out would slow them down significantly. 912